Per the ATF's FAQ, a buyer may arrange an out-of-state sale if he or she arranges to purchase the firearm through a licensed dealer in his own state. Read more on the FAQ page.
May an unlicensed person obtain a firearm from an out-of-State source if he arranges to obtain the firearm through a licensed dealer in his own State?
"A person not licensed under the GCA and not prohibited from acquiring firearms may order a firearm from an out-of-State source and obtain the firearm if an arrangement is made with a licensed dealer in the purchaser's State of residence for the purchaser to obtain the firearm from the dealer."
[18 U.S.C 922(a)(3) and (5), 922(b)(3), 27 CFR 178.29]
Read more from ATF's Code of Federal Regulations, Part 478 - Commerce in Firearms and Ammunition.