Quoted:
Legally, you would need to have an FFL in his state perform a transfer for you. Only FFLs can legally transfer guns between states. You can give it to the Ill. FFL in person, or you can send it to the FFL UPS/FedEx (but not USPS).
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A couple things to think about/clarify/support what was said above:
1) FFL's can transfer hand guns/long guns using USPS. Fill out form 1508 to do it. Priority mail dealer to dealer is fairly cheap. Long guns can go from private to FFL using USPS. Other common carriers can take long or hand gun from FFL/private to FFL in another state.
2) Dealers can always accept long/hand guns from anyone in the US, even over state lines. Private citizens can send long/hand gun to dealer anywhere in the US.
3) Executors of estates can transfer firearms to someone directly who lives out of state, without an FFL, providing the state they reside would allow it. See exceptions on out of state transfers for more information on this.
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