Ask him what he would be doing if his girlfriend wasn’t graduating. If he says he would be staying at the HS, I would discourage early graduation.
He hasn’t exhausted the possibilities academically or EC wise at his boarding school. You are paying for him to have those opportunities.
I’m not a Princeton adcom, but if he has not taken upper level courses and has no leadership EC positions, and is leaving HS early, I would be wondering why.