Should I [25/f] tell the person my X [27/m] cheated on me with about our relationship?

My X is, likely, still seeing/talking to this person. She doesn't know that he was dating someone when they met/hooked up. He begged me to remain friends with him after our short 2 months ended, so I did. His best friend told me about his cheating, not him. I knew him for a year prior. He began our relationship telling me that he had been in love with me, direct quote: "I'll wait for you for another 3 years if I have to." I have learned that he has cheated on every one of his girlfriends. He was seeing someone when we initially started hooking up. I am considering this a) because I'm beginning to realize a friendship with him is worthless, b) He could be leading this girl on too, c) and I seriously just want some good old fashion revenge. It's been a month since we broke up.