Yes. A person who lawfully possesses a firearm may transport or ship the firearm interstate when changing his or her State of residence. If using a moving company, the person must notify the mover that firearms are being transported.
Certain NFA firearms must have prior approval from ATF before such firearms may be moved interstate. He or she should also check State and local laws where relocating to ensure that movement of firearms into the new State does not violate any State law or local ordinance.
[18 U.S.C. 922(a)(4) and 922(e); 27 CFR 478.28 and 478.31]