Help... (Bare with me it's long)

Jess
Okay so bare with me ladies because this could be quite long. I've been with my boyfriend for nearly a year and he is the most important thing in my life.
A few days ago he got a message from a girl he used to be quite close with before we got together, I don't know why they stopped talking but he assured me it wasn't my fault, so anyways he got this text from her and he told me about it nearly straight away which was really nice of him, he talked to her for about 5 minutes, about 4 messages were exchanged and then he stopped replying because he knew a proper conversation would upset me, the problem I have with this is that I don't want him thinking he can't talk to someone he used to be super close with before he even met me, I'll admit I do get jealous because there were feelings involved on her side but I guess that's just something that happens. I really don't know what to do because every time I tell him he can talk to her as long as he at least me knows (might seem controlling but we're always honest with each other) he never believes me and always says its fine. I don't want to come across as a controlling girlfriend and I'm okay with him talking to another girl as long as it's not romantic or secretive, I want him to believe me on this but he doesn't seem to. What can I do? I know I'll be seen as a total bitch if I say no don't talk to her I'm jealous, but he won't accept me being okay with it 😕