Search Results: admitting mistakes

So my boyfriend recently made a female friend online who has a boyfriend but she is the flirty type. She's already told my boyfriend if things were diff. with both of them she would totally be in a long dis. relationship with him. She had msg'd him about her getting a pole and he responded flirtatiously by saying "I would love to see your legs wrapped around that pole swinging*blush*"
When I confronted him about this he admitted it was highly inappropriate and he had a 'moment of weakness' he said that it just felt 'easy' to do (he works a lot, doesn't have energy for sex sometimes) It's just that, that day we had sex! Even a shower together! and he sends a flirty message to her later, I don't understand. He said it was a mistake and he didn't tell me cause he felt guilty about it, he promised it won't happen again and I made it clear what would happen if it did. I could tell when we talked about it he shed some tears and I could feel the remorse. It seems like it was "just a flirt" but it really hurt because it was a friend not a stranger.
He said that he'd stop talking to her but I don't want to seem controlling telling him he can't be friends with her. He said, nothing is more important to him than our relationship, and it's not worth it interfering with us. He has admitted that he finds her attractive so when he sent it he was talking out of his dick, not his head/heart. He said he loves me and only wants to be with me and compared the attractive part to me thinking Brad Pit is attractive, like she's attractive but he loves me and would always choose me over her. Should I be comfortable with them being friends, or take him up on the offer for him to stop talking to her? Would this make anyone else very uncomfortable?
I told him he has to earn some of my trust back and he understands and wants to work to get it back. Am I justified to see his phone with his permission in order for him to gain my trust back/are there other ways he can?