Of course she can "press charges," meaning she tells the police that she wants you arrested, but whether you will be charged with a crime is another matter. Although every situation is different, in general an engagement ring is a conditional gift. It is a gift conditioned on the promise of marriage. So when the engagement is off and the couple won't get married, the person with the ring is supposed to return it to the other. Like I said, there are exceptions but this is a general rule. As such, if her ex was the lawful owner of the ring (and it seems like there's a good chance he is) then no crime was committed by returning it to him.
Of course she can "press charges," meaning she tells the police that she wants you arrested, but whether you will be charged with a crime is another matter. Although every situation is different, in general an engagement ring is a conditional gift. It is a gift conditioned on the promise of marriage. So when the engagement is off and the couple won't get married, the person with the ring is supposed to return it to the other. Like I said, there are exceptions but this is a general rule. As such, if her ex was the lawful owner of the ring (and it seems like there's a good chance he is) then no crime was committed by returning it to him.