Sounds like your H has made progress and is said that he wants to end it with OW and be with you. Take stock of the progress made and the baby steps. Its hard to do when you are in the middle of it.
I would stop checking the phone, it will drive you crazy. You should set a boundary with him that if you want to move forward, he should be more transparent with you to gain your trust back.
Me 38 H 39 M13 T18 S6 S9 Bomb Drop 11/11 Moved Out 7/12 Still have hope. No OW that I know of..