Is this respectable? Or is there something else going on (Texts below)

These are texts between my bf and his old hookup buddy. We fell out for 3 months. It was mutual but he initiated it. We didnt talk for 3 weeks, but then we still talked. but now we are working through it and have been going on a lot of dates and he admit its wrong to be friends with a girl he used to sleep with. I told him i cant do it if they’re still friends, because he was hiding the fact that they were still hanging out and texting and just the fact that they used to sleep each other. Theyre both 31, and mature about it, and had no sexual intentions. But still something felt shady. Im trying to leave all this in the past. He admit his wrongs, he said he cant lose me to anyone and he wants me and to build a life and family with me. We broke up in December, and he wants to work it out with me. He loves me a lot. Theres a lot more backstory but anyways. Is this message good enough? Can i move on past this? They never kissed or did anything like that. But were still close friends and that bothered me.

Also, they went to the movies like 2 or 3 times the past fee months. He also got her a birthday gift a fee weeks ago, and she ate with a friend and visited him at his job. And no they werent sleeping together. Just friends. BUT friends who used to fuck

She clearly doesnt respect our relationship. And only wont reach out so it wont start a problem, not because she respects our relationship. Ya, i dont like her. Me and him talked it out and i asked him a million questions just to be sure, and everything seems fine. I told him im willing to take things slow. I also said if you dont want to lose her as a friend, then dont remove her or block her, but just let me know so i can leave you alone. Shes blocked and removed now. He says he has no regrets and im all he wants. He said hes not upset about it because he would never want to lose me.

Heres an example of texts he sends me, that he sent me this morning

I also just met his sister the other day and hes been super romantic saying he wants to make me his wife and he asks me “what can i do to prove my love to you”

Seems like he lost me for a bit, and realized theres no other girl thats loves him like i have. He seems how valuable i am and he doesn’t want to lose me.

Note (there was never any cheating going on in our relationship. Our relationship was pretty healthy)

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