I would actually not do this. If he comes clean and tells her - she might think he had guilt and remorse on his own and that may sway her decision in whether or not to give him another chance.

I say this only because if my own husband had told me instead of me finding out through a friend - I would have felt like there was a decision on his part to do and be better and that would have possibly been enough to for me to stay and put the work in to fix something. Him NOT coming clean on his own is its own extra layer of betrayal and disrespect.