OP, is your partner employed? Some employers take a dim view of this sort of thing, particularly if he's posting under his real name.
Do you have children/does he have friends with children who have his as a friend on Facebook? He must be careful not to pass these images on to minors. Again, an employer would take a very dim view but so would parents.
Does he quite understand Facebook? It's not like 4chan or Reddit where you can be reasonably anonymous.
How long does he spend online? I don't know what to suggest really because when someone is this unaware they're beyond help really.