He writes her a "no-contact" letter, the content to be approved by you. In it, he says nothing romantic, but makes it clear that he wants to work on his marriage and they can have NO contact, ever again, and he asks her to respect his wishes. The letter gets delivered by you, or a 3rd party.
Transparency means that he changes his phone numbers, and gets detailed billing on the new cellphone, to come to YOU, and he gives you his daily schedule and checks in with you several times throughout the day. If he won't agree to these things, then he's not serious about trying to end it.
There is no "trying" to end contact. You either end it, or you're not SERIOUS about ending it.
