If it was, "I promise to give you a photograph of myself if you make a false statement," then she can just give him the photo.

If it was, "I promise to give you a photograph of myself if you make a true statement," then she could still just give him the photograph even though that makes the statement false. She didn't say she *wouldn't* give him the photo if he made a false statement.

He should try to make her say, "I promise to give you a photograph of myself if and only if you make a true statement." Note that the phrase "if and only if" often occurs in logic puzzles and mathematical proofs.