Additional note- unless YOU are a "licensed person"- meaning holder of a FFL, you may NOT TRANSFER any firearm to a resident of another state- unless THEY are a "licensed person". Includes rifles, shotguns, handguns, and anti-aircraft missles. Includes 'face to face". A DEALER can sell a rifle or shotgun to someone visiting from another state- a private citizen cannot- and that is spelled out quite plainly in Title 18 US Code, section 922.
The exception is not "gifting"- it is inheritance. The Executor of the estate acts on behalf of the deceased, and can transfer firearms to the inheritor without regard to their state of residence. When Dad died, he was a Virginia residnet, I was a Colorado resident. I recieved his firearms directly. This is also in 922.
Regarding shipping a firearm- whether by US Mail, FedEx, UPS, OR handing it to the baggage folks at Untied Airlines (that was not a typo) you MUST inform the carrier that the shipment contains a firearm. The Feds HAVE put folks in the slammer over this.
And you CAN ship or mail a rifle or shotgun to YOURSELF in another state- legally. Going to hunt at the Big Sky Lodge in Montana- I can mail my rifle, adressed to myself, in care of Big Sky Lodge. The ownership of that rifle did not transfer to another person.