How should I handle these false accusations?

Me and my ex had a very bad breakup, and yes there was a great amount of drama but we’ve talked it out and for awhile we were able to have civil conversations in text and over the phone. Lately someone (I believe its one of his close friends, who doesn’t like me too much.) has been telling him complete lies about me “trying to ruin his life” and saying I’m speading rumors about him. Last Monday, somebody hacked into his Facebook and caused some drama with his friends, and my name was brought up. Appearently I hacked into his facebook, I have no reculection of doing so whatsoever…in fact I’m pretty sure I DID NOT DO IT.

Bottom line we were “that couple” the ones who loved each other since 8th grade and deep down we still do. But its so hard to fix things when he keeps hearing these lies. I’m getting tired of constantly defending myself of these type of accusations especially because im innocent. I’ve talk to him about it and he says he “just needs time to trust” me again.

Is this drama worth it at all?
Should I keep repeatedly defending myself?
How much longer should I wait for him to “trust” me again?