Heart broken! Need advice!

Hello everybody! I'm really hurting right now, and would really appreciate some advices from you guys!

My boyfriend broke up with me in late June. We still live together due to the lease. I really want him back! We are in speaking term. He even toke me out for my birthday on Monday and bought me gift. However, my ex has been talking(mainly txting and msn) to this girl everyday since the break up. She's a common friend(I'm not close to her tho). I don't know what that girl told my ex, but she made my ex think that I was talking mad shit about him, telling other girls to stay away from him! In which I never did! I've never initiated any types of conversation with that girl until one day I was on facebook, she started talking to me, pretending to be my friend. All I did was to tell her how the whole situation made feel. She started to apologize and saying she'll stop taking to my ex if that's what I want. I told her I'm not a controlling bitch and I don't have the right to tell anybody who to talk to. That's it. I did save the whole conversation just in case. I don't want any bad blood between me and my ex, cos that will make getting him back impossible. However, I need to let him know what truly went on! How can I show him the conversation without making him pulling even further?

some additional infos: We will be moving separate ways by the end this month. We had a 2 yr relationship. I got really sick in the beginning of this year. He stayed with me the whole way thro and was telling me he loves me all the time. We had been planning on moving back to my home country together since Jan.

I would really appreciate your male point of view. I love my ex and I really wanna get back with him! Please help!