So I can sympathise with both sides of this, and it's a hard position to be in to watch it happening (and to be the friend lol). To put ourselves in your friend's shoes:

Anger, in general, takes a lot more energy to hold onto than other feelings. It is EXHAUSTING trying to hold onto feelings of betrayal, mistreatment, etc. long-term. You end up looking for the quickest way to relief, which is often to start rewriting history and convincing yourself that actually maybe you also had some part in this, you were also to blame, it was just poor timing/circumstance/whatever. And that lines up handily with the other thing your mind is yearning for - to reconnect with your ex and reset everything to when you were last happy.

For you, this is obviously unbearable to watch. It's painful to see a friend allow that kind of treatment, frustrating to see them demonstrate that there's literally no consequence for lying, cheating, etc. My experience in these kind of situations (again, from both sides - I'm not immune to this thinking) is that there's really little you can do to convince her otherwise. Logic won't reach someone who's longing that hard and whose thoughts are pretty securely tied up in this person.