Here's a quote from the ATF FAQ:
Transferring/Shipping/Possession of Firearms: 4.
- May I lawfully transfer a firearm to an individual who resides in a different State?
- What if the individual resides within the same State?
Under Federal law, an unlicensed individual is prohibited from transferring a firearm to an individual who does not reside in the State where the transferee resides. Generally, for a person to lawfully transfer a firearm to an unlicensed person who resides out of State, the firearm must be shipped to a Federal Firearms Licensee (FFL) within the recipient’s State of residence. He or she may then receive the firearm from the FFL upon completion of an ATF Form 4473 and a NICS background check. More information can be obtained on the ATF website at www.atf.gov and http://www.atf.gov/firearms/faq/unlicensed-persons.html. The GCA provides an exception from this prohibition for temporary loans or rentals of firearms for lawful sporting purposes. For example, a friend visiting you may borrow a firearm from you to go hunting. Another exception is provided for transfers of firearms to nonresidents to carry out a lawful bequest or acquisition by intestate succession. This exception would authorize the transfer of a firearm to a nonresident who inherits a firearm under a will or by State law upon death of the owner. See 18 U.S.C. § 922(a)(5)(A).
Link follows: https://www.atf.gov/resource-center/docs/0813-firearms-top-12-qaspdf/download
Bottom Line - no sales/transfers to a resident of another State without going through an FFL of the receiver's State of residence (with a couple of exceptions)
@Gabriel42 does the bold/underlined part affect the discussion we had the other day about transporting the gun to out-of-state FFL? Looks to me like this could be interpreted as it has to be shipped. The "has to be shipped" norm may have started with this.