All perfect praise be to Allaah, the Lord of the worlds. I testify that there is none worthy of worship except Allaah and that Muhammad, sallallaahu ‘alayhi wa sallam, is His slave and Messenger.
It is permissible for a man to shave the armpit hair of another man. Plucking the armpit hair is one of the Sunan of the fitrah (natural disposition). When plucking is intolerable, shaving is permissible. When one shaves another's armpit hair, this is permissible because the armpit area is not a part of the ‘awrah (bodily parts that must be veiled from others).
Allaah knows best.