Form G-639 and the instructions for that form are available at the USCIS web site at www.uscis.gov. The form is used to submit a request for a copy of your immigration file, pursuant to the Freedom of Information Act. The German Embassy is presumably asking you to obtain a copy of your immigration file so that it can be determined thay you have not become a U.S. citizen, since Germany generally does not permit dual citizenship.

You may also want to consider filing an I-90 Application with the USCIS, in order to obtain a new Permanent Resident Card ("Green Card"), unless you have a criminal conviction that could come to the attention of the USCIS and lead to the initiation of removal (deportation) proceedings after you go to have your biometrics taken and a criminal background check is performed by the USCIS as part of the process of renewing your Permanent Resident Card. Please schedule a consultation with an immigration lawyer for additional information and assistance.

G-639 is the form to request your immigration file under the Freedom of Information Act (FOIA). The German government probably wants you to prove that you did not obtain U.S. citizenship (yet). If you can prove your current permanent resident status (by renewing green card), wouldn't that be sufficient? You can ask the German Consulate. But you should be aware that you might have acquired U.S. citizenship by operation of law (if your parent(s) became a U.S. citizen when you were still under 18).

One could not come to expect less from the German consulate, a country which still does not recognize dual nationality, except where "expressly authorized" by its Gov. Jawohl!

What the Konsulat is in effect requesting that you do, as proof that you are in fact honest and did not secretly become a US citizen, is for you to file a Form G-639 "FOIA" application with USCIS, requesting the copy of your entire file in USCIS possession (and take it to the consulate once received from USCIS. )