OP this book might help you: Not Just Friends by Shirley Glass.
He should also read it. If he pretends that he gives a shit about you, and for his marriage. It contains strategies for avoiding affairs, which he needs to pay close attention to. Because he's either already banging her or very much intends to.
Nobody deletes totally innocent messages "just because you wouldn't like it", that's just a load of crap. The remaining messages are the ones he feels are "safe" to be seen.
Personally I'd be done at this point but if I wanted to give him one final chance, it would be totally cut her off on everything, no exceptions, no car parking space, and she doesn't come into the business. And I'd insist on him calling her right then and there so we could BOTH explain that as much as we don't blame her, I feel the friendship has crossed a boundary and that for the sake of his marriage and children, he won't be continuing the friendship.
I would not listen to any old bollocks about "Nooooo it's embarrassing" or "You'll humiliate her" - tough fucking shit, that's on him and his decision to spend 6 years - 6 fucking years! - taking the piss and eroding the trust that should be a bedrock of marriage. So yeah, he gets to feel embarrassed about that, and also to feel lucky and grateful to be given a last chance to catch himself on.
Even then, in all honesty, I wouldn't trust him further than I could throw him. I'd be expecting him to just get a second phone to carry it on. And I wouldn't want to live like that, so I'd be out, but I know with kids it's a big decision.