laws vary by state, but typically if he's legally able to purchase that firearm from a dealer, he can be gifted that firearm as a bona fide gift from immediate family members (the state in which he resides and the state where the transfer takes place may have some restriction on that which details the nature of the familial relationship). not that federal rules still apply to the gift, meaning no prohibited persons, if it's a controlled item (title ii) then the appropriate ATF form must be filed prior to transfer, et c. rifles and shotguns typically do not need special arrangements for gifting, but handguns sometimes do, depending on the state of residence and the state in which the transfer occurs.
as he's flying back to washington, if he wants to fly with the rifle he will need to have secure transport (locked hard case strongly recommended, and no you do not need "TSA" approved locks) and cannot keep ammunition in the same case as the firearm. firearm transport on aircraft should be declared during check in if it's not carry-on. carry-on usually must not be in a "ready to fire" state either, but that varies by specific airline.
he can also ground ship the firearm to himself. the package must be secure and sanitized of all "this is a firearm" obvious markings and cannot be shipped with ammunition in the same package. unlike handguns, you can ship a rifle or shotgun through the USPS, however handguns are restricted to common carriers only and typically require next day service when possible. the specific package carrier will have instruction available either online or in their store.