Cheated and told his girlfriend. How do I get him back?

Anonymous
Sorry this sounds horrible and yes i know it was wrong.
I cheated with a guy a while ago. He had a Girlfriend at the time. We started seeing each other for a while. I became angry because i couldn't handle him being with her. I told her everything we did and all the horrible things he said about her. Actually i messaged her on Facebook and told her. Also sending her screenshots of things he said to me in messages.
He was angry at me obviously. #1 they were living together. #2 he was saving money to move out (apparently )
She didn't actually see the messages until a few months later. I told her i said all the stuff because he rejected me and said i was lying. I told her the screenshots were fake and i made them up because i work in IT and can edit messages to look sincere. She believed me. Anyhow. They aren't together anymore. He was obviously angry at me.
13 months have gone by. How can i approach him and try and make amends. I dated him before she even started dating him. How do i get him back?

Cheated and told his girlfriend. How do I get him back?
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