You as an individual can not ship across a state line - you must have a licensed dealer in your state ship to a licensed dealer in the state where your brother lives.
and
You will need to find someone with a FFL on both ends to be safe, although you can always do a little research and may potentially be able to remove the bolt and legally ship the barrled action minus bolt to him with no FFL needed. You will need to do the research though. Then next visit he can pick up the bolt and hand carry it back.
Not trying to argumentative, but this is incorrect. This is directly from the ATF:
(B9) May a nonlicensee ship a firearm by carrier?
A nonlicensee may ship a firearm by carrier to a resident of his or her own state or
to a licensee in any state. A common or contract carrier must be used to ship a handgun. In addition, Federal law requires that the carrier be notified that the shipment contains a firearm and prohibits common or contract carriers from requiring or causing any label to be placed on any package indicating that it contains a firearm. [18 U. S. C. 922( a)( 2)( A) and 922( e), 27 CFR 178.31]
(B8) May a nonlicensee ship a firearm through the U. S. Postal Service?
A nonlicensee may mail a shotgun or rifle to a resident of his or her own state or
to a licensee in any state. Handguns are not mailable. A common or contract carrier must be used to ship a handgun. A nonlicensee may not transfer any firearm to a nonlicensed resident of another state. The Postal Service recommends that longguns be sent by registered mail and that no marking of any kind which would indicate the nature of the contents be placed on the outside of any parcel containing firearms.
Now he can certainly use an FFL on each end if he wants to avoid the hassle of shipping himself, but it will almost certainly cost him more money.
The absolute best thing to do is to call the FFL which will be receiving the firearm and have them instruct you on what to do.