Only if the abuse rose to the level of serious criminal behavior. Even then, I think it would only be a true obligation, if you knew that he uses contact with people whom he dates to get access to children he criminally abuses. If the abuse he meted out to me didn't rise to the seriousness of something I would file a police report about, then I would tend to think I should just mind my own business.

I might tell the new partner about behaviors like the following: He broke my jaw. or He stole my identity info and then wiped out my bank accounts.

That's an interesting question you raise.

It doesn't sound like this guy is a true predator in any criminal sense. If that is the case, then your main concern now is extricating yourself emotionally from this relationship. To a certain degree, only time will do that. I think you can help by telling yourself that how he interacts with his current girlfriend is really not your concern. It's only human to be curious. Indulging that curiosity in a small way is no big deal, but that should taper off as time goes by. Otherwise, you are letting the past contaminate the future.

I hope it gets easier for you.