You don't really own the firearm, you just paid for it. The paperwork is the process of changing the ownership.
Assuming your FFL agrees, you can sell the firearm, but the FFL has to make sure that it is not a straw sale, so selling it out of the area would be better. It could be assumed that anyone local is buying it for you and the FFL should not take a chance with that.
Did you have it shipped in or did you buy it from the FFL doing the transfer? If you bought it from the FFL doing the transfer, the FFL might not want you to sell it and make money, but they could refund your money.
FFL Transfer/Special Order Dealer since 1993.
Net-FFL list maintainer.
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