Simple answer- have the buyer find a US agent that can export the gun legally to him (companies that do that, and it is not cheap). He sends you money, you deliver it to his agent. Done.
YOu could not sell it to him directly if he came to your state. FEDERAL law says a private citizen may only dispose of a gun to a resident of his own state, or an FFL in any state.
FWIW, yes, an alien CAN buy a gun from a DEALER. For instance, if he has a hunting license.
What we have here is... failure- to communicate.