Ex best friend going after boyfriend

Last year my best friend decided to have nothing to do with me and my group of friends. She decided at her new school she was going to be popular and have a boyfriend and I don't think we were good people to be associated with in order for her to do this.
Recently I went into my first kind of serious relationship, 3 months on it's going well but I think my old best friend is kind of jealous. At a party we were recently at, she had her arm around him and posted a picture of them online afterwards. She sits next to him in maths and they have fun together because she's genuinely very nice and pretty and clever and sporty.
A few days ago I accidentally saw his phone screen and he was replying to her facebook message, it seemed like a conversation but I only had a quick glance because I'm not a prying person and it was accidental as I was looking at something else.
What should I do?

It seems like a tough situation to do anything without looking bad to your boyfriend.

Her putting her arm around him is a bit worrying but I don't think telling him that will do much good - he might just get defensive or criticise you (though you're right to be alarmed by it).

I think it might be an idea to slip into a conversation something like 'do you know how .... is doing at her new school?', and you could try to read his reaction to this - if something's up he might say something like 'no I don't really speak to her much', or if nothing's up he might be honest and say that they do talk a bit and she's doing okay, etc.

And maybe further on down the line (whenever you feel like it's right to) you could talk to him and say 'look, I'm not even suggesting forcing you not to talk to her but sometimes I feel like she's coming onto you too strongly and this makes me uncomfortable' (and mention the photo and anything else that may or may not have happened by then, but NOT the fact that you've seen them talking on facebook).

Thanks for the response I'm going mad here!
We're all at the same school now, I decided to move there last minute. They sit together in maths, she knew him before me and they get on well. I think she liked him and vice versa a little bit but then she lost interest.

He's not done anything wrong it's just she's always been the one out of the two of us that guys go for... It would be hard for a guy to say no if she threw herself at him if you know what I mean?