[24 F] [24 M] My bf’s female friend called him “love”. He has a past of lies. What to do?

Just to give you context:

1)Me and my bf are in our “second” relationship which means that we had a relationship for over a year that came to an end because he compulsively lied about everything (girls, smoking, where he was, etc.). We broke up for a year and after he showed how he changed we got back and we are together for six months now.
2) We are 24 years old and my bf has a college female friend since 19 years. I never had anything to say about her until the moment (during our first relationship) when she talked about the breast implants she was going to put to my bf, including size and other details, etc. I thougth that was innapropriate and at the time he never recognized that. Later, he did recognize and said that was innadequate from her to talk in that extense about that to him. From other situations that happened meanwhile, I have the firm belief that this girl has a crush on my bf.
3) I had nothing to say about his behavior until yesterday when I saw him too focused on his phone all night while we were at the shopping and he didnt even talked to me a lot the whole night. I found that odd and in the end of the night I asked him to show me his phone. (I never ever touched his phone without his autorhorization, so I politely asked). In one of the chats he showed me there was his female friend (the same as the breast implants) thanking his birthday whishes saying “i like you very much” and calling him “love” which in my country and translated is something you only call to romantic partners, but not to friends. And is something I never saw her calling him in the past at least.
I started to ask him why did she call him that and if something had happened between them that I should know. He said he didnt know why she called him “love” and that nothing happened and that this was the first time she called him this even tough they are friends for 5 years.
Adding to this, I have to say he has been a very jealous partner since we got back together so he immediately answered yes when i asked him if this would bother him if it was a friend of mine calling me that name and treating me that way.
I have to say I started this relationship, trusting him but knowing up front that he has a past of lies and ommissions and that cannot be erased. I am worried that this is one more lie from him and that is happening something between them that Im not aware of. I generally trust my gut feeling for everything but in this case I think my gut feeling can be tricked by what happened in the past and thats why Im here asking for some advice or opinions from you.
Thank you in advance.