The rifles are pretty straightforward, the handguns are tricky.
They are his rifles, so he can mail them to himself in another state. That is okay by federal law, state and local law may differ.
The problem with handguns comes up because a non licensed person may not use the postal service to ship anything other than a rifle or shotgun. UPS and Fed Ex internal regulations say that you cannot ship a firearms to anybody other than an FFL.
So, you can box up the rifles and shotguns, with your brother's name as the sender and the recipient, and legally mail them.
6. May I lawfully ship a firearm to myself in a different State?Any person may ship a firearm to himself or herself in the care of another person in the State where he or she intends to hunt or engage in any other lawful activity. The package should be addressed to the owner “in the care of” the out-of-State resident. Upon reaching its destination, persons other than the owner must not open the package or take possession of the firearm.
https://www.atf.gov/resource-center/docs/0501-firearms-top-10-qaspdf/download