No receipts required. A lot of states still allow private party sales (without FFL involvment). These are cash sales with no receipt and people move from these states all the time, so the Dept. of Justice can't expect receipts. I do not think the form asks for a receipt? Have you looked at the form?
If I were her, I would just fill out a registration form and send it in. If it asked when she moved, fill in the true date. I am confident there will be no problems. (Just don't ask me to post bail.
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George