Yes, you can mail the power of attorney document directly to your brother and he can get it handled inside. This is more common than people expect and correctional facilities have a process for it.
Once the document arrives through the mail, your brother needs to request access to a notary through the facility's main office or administrative staff. Most prisons and jails have a notary available on staff or can arrange access to one, specifically because legal documents like power of attorney forms require notarization and inmates have legitimate legal needs that cannot wait until release.
The entire process from the time he receives the document to the time the notarized form is ready to be mailed back typically takes about two weeks. That accounts for the time it takes him to request the notary appointment, get it scheduled, complete the signing, and get the document back out through the mail.
A few practical things worth knowing before you send it. Make sure the document is complete and correct before it goes in the mail, because any errors that require a new form will restart the clock. Include a self-addressed stamped envelope if you want him to mail it back directly to you, which speeds up the return process. Send it through InmateAid or certified mail so you have confirmation it reached the facility.
Legal mail is generally processed with more care than standard correspondence at most facilities, so flagging the envelope as legal mail on the outside can help ensure it gets to him intact and promptly.