I can't imagine that they have any professional need for contact outside of work.
H can also take the initiative and quietly invite a few of the GUYS out for a beer when nothing has been planned. No one is going to question him excluding PW. They aren't dopes.
The fact is, there is no reason he can't have a life that exclues PW outside of work if he chooses to do so.
He can block her phone number on his phone. When he starts in on his crap about not understanding you why it bothers you, stop that cold:
"H, you and I both have acknowledged that your R with her was inappropriate and damaging to our M. Cut the crap. I am NOT willing to accept you continuing to interact with her outside of the office. It is inapproprite for you to be her friend or rescuer. She is not a friend to our M, you should not be a friend to her. I am not willing to negotiate about this. Your contact with her hurts me and our M. Your lying about it and concealing it is doubly undermining. That is sufficient reason for it to stop completely immediately. I want you to call her on speakerphone and deliver this message to her crisply and directly. Then, stop contact as you have agreed to do."
