High school is an accredited institution. Because he was enrolled for at least 5 months of the year, they qualify as your dependent. The dependent's earnings do not matter. The main thing is that the dependent did not provide more than half of "their" "own" support. Also, time spent away from home for the primary purpose of attending school is considered to be time they lived with you. So make sure you indicate they lived with you the entire tax year.
If the dependent files their own tax return, they must select the option for "I can be claimed on someone else's return". If they qualify as your dependent, it doesn't matter if you actually claim them or not. They don't have a choice in that.
