Should she know?

So my ex and I broke up over a year ago after a four year relationship and engagement. We had bought a house a year and a half before that so due to tax reasons I've had to stay in the house and live with him. (Sucky) The reason we broke up, he says he was happy but I knew it was for a friend of his. Well he says they aren't officially dating, she is out of state at school for the next two years, however they skype and tell each other 'I Love You' and exchange naked pictures and videos. Anyway, so here he and I are still sleeping together and hanging out and basically dating just no official title but obviously I know about her and yet she has no clue that we still live together much less hang out and have sex. I want to tell her. I believe she should know. Not only so she will realize what type of guy he is but also she deserves to be heartbroken because they fooled around for months before he actually got the balls to break up with me. I know this seems childish but I think about telling her all the time. If I would tell her it would have to be some sort of anonymous email cause otherwise it would cause hostility in the household. I'm just not sure what to do. Help!