@woodcutter I’m not a lawyer, and I suspect that fraud laws vary somewhat by state. The elements of common law fraud can be found here, however, and it seems the only one that would be difficult to prove is this person’s intent to use his claimed rank to defraud you. There is also a link near the bottom of the article to 18 U.S.C. ยง 704, which addresses false claims of military decoration. The code doesn’t explicitly mention claims of rank, but it may cover physical representations of rank. As you are more familiar with both the military and the situation at hand than I, you are better situated to spot some part of the law he violated.
I wish you the best of luck in pursuing this. Since fraud is both a criminal and civil offense, you might go to the police and see if they are interested in pursuing the case. They might then be able to gather evidence that you could not get on your own—evidence you could later use in small claims court or otherwise.