This is something that happens through teen years but it doesn't stop it hurting. I remember easy child going through this - her best friend was very easily 'won over' by other girls and through primary school would sometimes avoid easy child because another girl had told her she had to, "If you want to be my friend."
This girl was also very gently, very caring - but very insecure, she was always scared of hurting people and would choose the path of least resistance; she perceived easy child as someone who could cope better without her for a while, than the mean girl putting the emotional thumbscrews on her.
easy child coped in two ways:
1) She let her friend know that she WAS hurt, that she understood the dilemma but felt honesty and honour should have been valued more highly and the 'mean girl' told to stop the emotional blackmail.
2) She didn't cut off her friend, but she did make new friends while she waited for mean girl to lose interest in manipulating their friend and leave her to find her way back to easy child.
easy child has moved on well in life. Her friend is still a bit of a professional drifter, always concerned about what people think about her and scared tat people mightn't like her. "Mean girl" became promiscuous and got involved in drugs (not in a big way, just enough to escape the parts of herself she doesn't really like) and professionally has amounted to nothing. She still manipulates people, including her parents.
And for something I did in a similar situation, back when I was young - I made friends with my rival. Genuine friends. That way, I wasn't too dependent on just one person as kindred spirit, I had more possibilities. It also meant I got included more when friends in common got together. Getting out and about in a small group is healthier in so many ways, rather than a too-close friendship with just one other person, which excludes everybody else for both of you.
If this isn't really possible or won't work (as it wouldn't have for easy child, because 'mean girl' was very jealous of easy child's apparent self-confidence and brains) then there is a different pathway. First, she has to learn to be her own best friend - she needs to learn to value herself. Not easy at 13. Then she needs to find another friend to share this with. begin slow and gentle, invite another girl around for an informal craft session (perhaps making Christmas cards or scrap-booking). Or invite a friend around to watch a classic chick flick.
In the meantime, keep in friendly touch with earlier friends but make it very clear she isn't being needy, she is happy for the new friends to get to know one another, she will get on with other interests while she waits for them to get over all this.
OK, she might have to pretend a little, but this will work. To be attractive as a friend you need to seem as if you don't need or feel desperately about wanting friends. You need to project confidence and love for everyone. The popular girls aren't always the pretty ones or the smart ones, they are the ones who make other people feel good and emotionally pampered, but with honesty. When you talk to a good friend who makes good eye contact, who seems genuinely interested in you, who asks you how you are and means it - you become someone others will seek out for a friend.
And if she practices these skills on friends, she will also reap the benefits later on when boys really get big in her picture!
I hope she can feel better over this - but to openly get upset over this is not going to help her relationships. Avoid seeming jealous, because only someone who is needy, needs to be jealous. And the more jealous you seem, the less inclined people are to want to be friends - they could be the next target. Think of what our perception is of what a jealous person looks like, or sounds like - do you want to be around someone like that? Few people do.
So finding ways to turn any jealousy into something positive is going to work so much better in so many ways. And often, it also changes the feelings themselves, if you can change other manifestations of the jealousy.
I gave up jealousy 35 years ago, when an ex-fiancé tried to make me jealous with his new girlfriend. I noticed his look of triumph when I expressed curiosity about the girl, so I did the only thing I could do - I made friends with her. If I was curious about her, I would find out from the horse's mouth and not from the horse's ****. And in the end, she & I spent so much time chatting, she had no time for him - it was delicious! She was a really nice person, we got on very well. I could have burned a lot of emotional energy on hating her, but instead of constantly feeling angry and mean inside, I was happy with a new friend and every day realising more that my former creep of a fiancé was good riddance - for both of us.
Doing the unexpected, being warm and generous - it feels good and other people like to be around it.
Walk in the sunshine, not in the dark.
Marg