HOWARD, Circuit Judge.

A jury in the District of Massachusetts convicted the appellant, John Davis, Jr., of aiding and abetting the making of a false claim against the United States in connection with his 2008 federal income tax return. See 18 U.S.C. §§ 287, 2. In this appeal of his conviction, Davis alleges that the district court's aiding and abetting instruction was incorrect as a matter of law, that the instruction also constructively amended the indictment in violation of the Fifth Amendment, and that the evidence adduced at trial was insufficient to sustain his conviction. After careful review, we affirm.

I.

For purposes of the sufficiency claim, we recount the facts in the light most favorable to the verdict, United States v. Howard, 687 F.3d 13, 15 (1st Cir.2012), deferring some details to our analysis of the specific issues raised on appeal. In early 2009, the Internal Revenue Service received a 2008 Form 1040 federal income tax return, filed electronically on behalf of John Davis, Jr. of 11 Oakhurst Street, Apartment 1, in Dorchester, Massachusetts. The return reflected an adjusted gross income of $2,586 earned from "bingo lottery gambling winnings," and claimed a refund of $7,390 based on a "first-time homebuyer credit."

Applicable to homeowners who purchased their initial primary residences between April 8, 2008 and December 1, 2009, the federal first-time homebuyer credit authorized a tax credit of 10% of the purchase price, up to a maximum of $7,500. To obtain the credit, and any refund that may result from it, the IRS required a qualifying purchaser to submit an addendum — Form 5405 — with the purchaser's federal income tax return providing additional detail concerning the claimed credit. Davis's Form 5405 stated that he purchased the Dorchester apartment on March 18, 2009 for $73,900 (home purchases in 2009 were eligible to be claimed on 2008 returns). The IRS processed the return and issued a $7,390 refund check made payable to Davis, who cashed the check, retained $1,000 for himself, and gave the balance to an undisclosed recipient whom he later described to investigators as his "tax preparer."

After a more thorough review, the IRS determined that the owner of the Dorchester apartment was not John Davis, Jr., but his mother, Greta Davis and that the property had been purchased by Greta long before April 8, 2008, thus precluding eligibility for the first-time homebuyer credit. When IRS agents subsequently visited the appellant, he initially denied any involvement with the filing, intimating that it had been submitted without his knowledge. Upon further questioning, he acknowledged that the tax return accurately reported his personal information, that he had provided the information to his tax preparer — whose identity he declined to disclose — for the purpose of filing his tax return, and that he had never purchased the Dorchester apartment. He also admitted to cashing the check, keeping $1,000 for himself, and giving the remainder to the unidentified preparer.

Shortly thereafter, a federal grand jury in the District of Massachusetts indicted Davis for making a false claim against the United States, 18 U.S.C. § 287, and aiding and abetting the same, id. § 2.1 Following a two-day jury trial, Davis was convicted of aiding and abetting, for which he was sentenced to one year of probation and ordered to pay $7,390 in restitution. This timely appeal ensued.

II.

The court instructed the jury as follows on the aiding and abetting charge:

(emphasis added).

After deliberating for roughly ninety minutes, the jury sent out a note with three questions, two of which are germane to this appeal. The first question related to the substantive charge in the indictment: "[a]re we deciding whether the defendant made a false claim to the U.S. government, or are we deciding whether he specifically and knowingly filed a false claim re: the first time homebuyer's credit[?]" (emphasis in original). After discussion with counsel, and over the government's objection, the judge instructed the jury that Davis "would have to know at the time the return was being filed that the false claim involved the first-time homebuyer tax credit, because that's what the indictment as it is framed alleges, and that is the false claim alleged to have been made on the return itself."

The jury next asked, with respect to the aiding and abetting charge, whether Davis "[m]ust ... have known that the tax preparer was fraudulently filing the first-time homebuyer tax credit specifically?" The trial judge's initial response was similar to the view given for the substantive charge. In discussion with counsel, the court observed that, "given the way the case is indicted, again, they'd have to find that [Davis] aided and abetted the principal with the intent of seeing that a false claim was filed with regard to the first-time homebuyer tax credit." The government objected, arguing that the aiding and abetting charge only required proof that Davis knew that "a false tax return" was going to be filed. Davis agreed with the trial court's formulation. The discussion concluded with the judge rejecting the government's position.

After a recess, however, the court changed tack, ruling that Davis did not need to know "the particular details of the falsity, but he has to know that it was false, it was intended to be false, so that he shared that intent with the principal." The judge relied on United States v. Garcia-Rosa, 876 F.2d 209 (1st Cir.1989), vacated on other grounds by Rivera-Feliciano v. United States, 498 U.S. 954, 111 S.Ct. 377, 112 L.Ed.2d 391 (1990), observing that "a culpable aider and abettor need not perform the subject offense, be present when it is performed, or be aware of the details of its execution." After acknowledging the defense's objection, the court answered the jury's question as follows:

The judge concluded by asking the jury whether his answer was clear, to which one juror replied "no," and asked, "[s]o in terms of a false return, would he have to know that it was specifically going to be false relating to the first-time homebuyer tax credit?" The court answered:

After less than an hour of additional deliberation, the jury returned its verdict, acquitting Davis of the substantive offense and convicting him of aiding and abetting.

Following the verdict, Davis renewed a Rule 29 motion for acquittal that he had made orally at trial. He reiterated his argument that the aiding and abetting instruction was erroneous because it did not require the jury to specifically find that he knew the tax return was false with respect to the homebuyer's credit. The district court denied the motion, United States v. Davis, 828 F.Supp.2d 405 (D.Mass.2011), concluding that there was "no dispute that the evidence at trial established that Davis was a willing participant in a scheme to file a false 2008 federal tax return." Id. at 406. The court's ultimate ruling was premised on its underlying observation — as reflected in the answer to the jury's question — that an accomplice is responsible for all of the natural and foreseeable consequences flowing from the common scheme. Id. at 409. Thus, the court held that the conviction was proper because the evidence supported the jury's finding that Davis shared the tax preparer's intent to file a false return and because the reliance on the homebuyer's credit was reasonably foreseeable to Davis.

III.

Davis makes three separate arguments on appeal. First, he asserts that the district court's aiding and abetting instruction was legally incorrect. Relatedly, he argues that the instruction constructively amended the grand jury's indictment, in violation of his Fifth Amendment rights. Finally, Davis claims that the evidence was insufficient to support an aiding and abetting conviction.

A.

We review de novo the claim that the trial court's jury instruction was erroneous. United States v. Godin, 534 F.3d 51, 56 (1st Cir.2008).

The underlying premise of Davis's jury instruction argument is that the substantive crime with which he was charged was "filing a false Form 5405 for a First Time Homebuyer Tax Credit." Therefore, he argues, a proper aiding and abetting instruction would have required the jury to find that he had specific knowledge of the filing of the homebuyer credit form. We disagree.

Davis was charged with aiding and abetting a violation of 18 U.S.C. § 287, the elements of which are: 1) presenting a false or fraudulent claim against the United States; 2) presenting the claim to an agency of the United States; and 3) knowledge that the claim was false or fraudulent. See United States v. Clark, 577 F.3d 273, 285 (5th Cir.2009); see also United States v. Drape, 668 F.2d 22, 26 (1st Cir. 1982) ("Where a tax return is filed with the `guilty, actual knowledge that it was false,' the jury may infer the requisite intent to [violate 18 U.S.C. § 287]." (quoting United States v. Rifen, 577 F.2d 1111, 1113 (8th Cir.1978))). Aiding and abetting requires proof that: 1) the substantive offense was actually committed; 2) the defendant assisted in the commission of that crime or caused it to be committed; and 3) the defendant intended to assist in the commission of that crime or to cause it to be committed. United States v. Rodríguez-Adorno, 695 F.3d 32, 42 (1st Cir.2012). Moreover, as the district court correctly observed, a "culpable aider and abetter need not perform the substantive offense, be present when it is performed, or be aware of the details of its execution." Garcia-Rosa, 876 F.2d at 217. Although Davis alleges that the substantive crime with which he is charged is filing a false Form 5405, this in fact only represents a detail of the execution of the actual crime that he aided and abetted: making or presenting a claim upon the United States "knowing such claim to be false, fictitious or fraudulent," in violation of 18 U.S.C. § 287. The district judge was therefore under no obligation to instruct the jury that it had to find that he had specific knowledge of the filing of the false Form 5405 to convict him of aiding and abetting. See United States v. Hernandez, 218 F.3d 58, 65 (1st Cir.2000) (observing, in affirming conviction for aiding and abetting drug distribution charge, that defendant's knowledge of the particular controlled substance being distributed is not necessary); United States v. Loder, 23 F.3d 586, 591 (1st Cir.1994) (holding that government need not prove that defendant was aware of all the details of the fraud to sustain a conviction for aiding and abetting mail fraud). The aiding and abetting instruction given here accurately conveyed the appropriate legal elements.

In support of his challenge, Davis cites cases and rules that establish the contours of a legally sufficient indictment. E.g., Fed.R.Crim.P. 7(c) ("The indictment... must be a plain, concise, and definite written statement of the essential facts constituting the offense charged...."); Hamling v. United States, 418 U.S. 87, 117-18, 94 S.Ct. 2887, 41 L.Ed.2d 590 (1974) (holding that statutory language in an indictment "must be accompanied with ... the facts and circumstances as will inform the accused of the specific offence" and "enable[] him to plead an acquittal or conviction in bar of prosecution for the same offense"). But these authorities address the sufficiency of indictments, while the instant appeal challenges the court's jury instructions. As the government suggests, Davis's argument confuses the purposes of indictments and instructions. The purpose of the former is to provide a defendant with adequate notice of the charges against him, see Cola v. Reardon, 787 F.2d 681, 700 (1st Cir.1986), while the function of the latter is to convey to the jury the legal elements required for conviction. Harrington v. United States, 504 F.2d 1306, 1317 (1st Cir.1974). The trial court need not use the precise words proposed by either party in its instructions; it is sufficient if the principle of law is correctly stated. Id.

"The function of the appellate court with respect to jury instructions is to satisfy itself that the instructions show no tendency to confuse or mislead the jury with respect to the applicable principles of law." Id. We are so satisfied here and find no error in the district court's aiding and abetting instruction.

B.

Davis next argues that the district court's aiding and abetting instruction constructively amended the indictment. "A constructive amendment occurs when the charging terms of the indictment are effectively altered by the prosecution or the court after the grand jury has last passed upon them." United States v. Rodríguez-Rodríguez, 663 F.3d 53, 58 (1st Cir. 2011), cert. denied, ___ U.S. ___, 132 S.Ct. 1592, 182 L.Ed.2d 204 (2012). While a constructive amendment is prejudicial per se and requires reversal, United States v. DeCicco, 439 F.3d 36, 43 (1st Cir.2006), we conclude that no such amendment took place here.2

This argument, like Davis's instructional error claim, depends on his underlying premise that he was charged with filing a false homebuyer tax credit claim. Thus, he argues, the jury instructions allowed him to be convicted for aiding and abetting some other "false claim," other than the one in the indictment. As a matter of law, this argument fails because, as we have noted above, Davis was charged with aiding and abetting a violation of the False Claims Act by presenting a false claim, not with "filing a false tax credit claim."

The argument also fails as a factual matter, as there was no evidence presented of any other falsity in the tax return other than the filing of the Form 5405. Davis therefore could not have been convicted for aiding and abetting the filing of anything different than that alleged in the indictment. Accordingly, no constructive amendment was effected. Cf. Stirone v. United States, 361 U.S. 212, 218-19, 80 S.Ct. 270, 4 L.Ed.2d 252 (1960) (holding that an indictment was unconstitutionally broadened where prosecution offered evidence of two theories of liability — interference with interstate sand shipments and interference with interstate steel shipments — but grand jury indicted defendant only on the first theory).

C.

Davis's final assertion on appeal is that the evidence at trial was insufficient as a matter of law to support the aiding and abetting conviction. As noted, the district court rejected this argument in the context of Davis's Rule 29 motion. We review the denial of that motion de novo, examining the evidence in the light most favorable to the verdict to determine whether any rational juror could have found the disputed facts beyond a reasonable doubt. United States v. Savarese, 686 F.3d 1, 8 (1st Cir.2012).

Here again, Davis's initial foray erroneously narrows the charged crime to aiding and abetting the filing of the Form 5405. Having already rejected that position, we assess whether the evidence was sufficient to permit a rational juror to find that Davis aided and abetted the tax preparer in filing a false claim. We hold that the evidence was sufficient.

There is no dispute that Davis's return contained a false claim for the homebuyer tax credit to which he was not entitled. Thus, the first element of the charged crime — that the principal actor committed the substantive offense — is easily satisfied. See U.S. v. Gonzalez, 570 F.3d 16, 28-29 (1st Cir.2009).

Similarly, the evidence was sufficient to support the other elements — that Davis knew that his 2008 federal tax return contained a false claim and that he helped the principal, the tax preparer, file the false claim. See Rodríguez-Adorno, 695 F.3d at 42. The jury could have found that Davis willingly gave his name, address, and telephone and social security numbers to the preparer, although he refused to identify that person to law enforcement. The jury also was aware of the odd fact that Davis had provided only biographical information to the preparer, but no financial information. Davis subsequently cashed a $7,390 IRS refund check, of which he gave all but $1,000 to the un-named preparer. Finally, given the evidence of Davis's paltry income and the fact that his prior years' refunds were considerably smaller than $7,390, the jury could have inferred from his payment of the lion's share of the 2008 refund to the preparer that the two had an arrangement regarding the false claim. In light of this factual record, the verdict was supported by the evidence.

IV.

Davis's conviction is affirmed.