You could just ask him outright if he's been at all in contact with her in ANY WAY.. be sure to phrase this right, he seems to think REPLYING to a facebook post isn't contact lol
I just don't know how he would take that, but i suspect he would get defensive, which again usually indicates cheating in underway.
If he refuses transparency there's no reason to think the afair is over.. and I would even tell him that outright.
The mistake here is that he muddled into a verbal no contact arrangement with you, but no transparency plan was forthcoming or insisted on by you either.
So, you are basically taking him at his word that he's being honest... With an addict this is usually NOT a good idea...