Federal law prohibits the direct purchase of firearms by purchasers who are not residents of the state where they are buying the gun. It has to be shipped to a licensed dealer in the purchaser’s home state. If I buy a firearm from PSA when I am driving through South Carolina in a few months, I would have to pick it up from the local gun shop when I get home. No taking potshots at SC and NC signs unless I bring along my Red Ryder carbine action 650 shot range model air rifle. And yes, I will be wearing eye protection, so don’t say it.
1968 GCA: One can purchase a handgun only from a dealer in your state of residence. Long guns can be purchased from a contiguous state to your state of residence. So, yeah, if you buy one on the road someplace that dealer has to send it to your hometown dealer.
In Trump’s particular case, since he’s under indictment, he can’t sign the 4473 form in any state. Melania could take possession if they actually want the thing.
As a side shot, Trump was already known to “carry” before he was Prez. The SS guys talked him out of his own. But I expect he still has an ace someplace.