As has been mentioned, if he purchased a serialized lower and ASSEMBLED the rifle, then he did NOT manufacture the firearm, so the "manufacture for private use" law you reference does not apply.

HOWEVER, if he ASSEMBLED the rifle with no intent of personal ownership, and built it for profit, he DOES have to have a business license and FFL to be able to do so legally. Even doing ONE rifle for profit. Lots of guys slip stuff under the radar for personal businesses which SHOULD be on the radar, in the trade, they call that tax evasion. I wouldn't mess with federal laws just to help transfer an AR-15 to let your brother make a few bucks, and he shouldn't be messing with it without the right legal steps taken. I got in trouble with the BATFE about 18yrs ago because I was ASSEMBLING AR's for profit, under a business license, but didn't have an FFL - technically, doing so made me a firearms dealer and gunsmith... Luckily they let me suspend operations, pay a fine, and apply for my FFL to continue operating. Even after 1 firearm, as it's a business dealing in firearms for profit. Even if the owner purchases and provides the serialized lower, you still have to have an FFL, because to operate the ASSEMBLY business, whether for profit or not, you're performing business as a gunsmith - which has it's own FFL type. Unless your brother has an FFL and a business license, what you described is a state AND federal offense - he has to have a business license to operate as a firearms dealer and gunsmith for profit (his labor charges) on the state/local side, and has to have an FFL as a firearms dealer and/or gunsmith to be able to perform the assembly business for profit on the federal side.

Out of state private transfers are tricky, and largely vary state by state. Some states only allow their citizens to purchase firearms in their home state, or contiguous (bordering) states. Some states require FOID or other pre-purchase requirements for owning firearms, or at least certain firearms. I saw Minnesota mentioned above, I do know to purchase an AR-15 in minnesota, you do have to apply for a permit of some sort, and have certain restrictions on firearms (number and/or type)... So that might not be an issue for YOU, but it could be if you facilitate the transfer of a firearm to an illegal recipient.