Foreign Office and Turkish Embassy advice would suggest that a new passport is required, but I personally have no idea how stringently Turkey enforces this minimum passport validity requirement.
However, if he does decide to renew his passport now, he would have the unexpired period transferred from the old to the new passport.
For info and advice about passport applications and renewals, we have a separate
PASSPORT Q&As topic where a member of Identity & Passport Service staff regularly gives advice. However, that is a general topic about UK passport matters, not related to specific entry requirements for Turkey which are best discussed here in this topic.
David