How to deal with jealousy and distrust?

Greetings fellow souls, Recently, I was broken up with by my boyfriend of around 9 months because he thought I cheated on him. The only problem is that I didn't, nothing. No flirting with intention, kissing, touching, etc. nothing. Just some theories he created in his head and couldn't get over. Throughout the entire relationship, he was highly jealous and possessive, so I assume his untrusting behaviour and his unwillingness to believe me spawn from that. When we broke up, his behaviour was incredibly rude, he hit me in the face, insulted me, tried to get me to have sex with him and generally humiliated me in any and every way possible. I understand that the only real solution to this is to move on, and I am working on that moment by moment. My question is how do I get over the him thinking I cheated aspect? I seem to have this incessant need to end things well and I despise the idea of him walking around telling lies about me and feeling like a victim, when I'm the one who was hurt and wrongly accused. Despite all the troubles our relationship had, there were many excellent moments and I still harbour tender feels for those times. So essentially, how do I get over being wrongly accused? Is it low of me to even care? Our relationship clearly had to end, I just wish it wasn't in anger and bitterness.

Part of me wants to tell not to give a flying fish about anything he thinks, to pick up the pieces of your life he's left you with, and move on with your life. Part of me understands the need to feel vindicated, especially when you did nothing wrong. But this is the thing- if HE thinks you're cheating or that you cheated, that's the story he's going to go with! Unfortunately, there isn't anything you can do to change that. And because of that, you will have to be okay with that, and that's the only way you can get over being wrongly accused. As much as we want them to, all our relationships won't end well. This is one of those cases.