you believe she is only interested in sex with you for the hope that it would make your friend jealous. this friend whom she is struggling with getting over a break-up with. and you have personal knowledge that it won't make him jealous because he maintains no feelings for her, but she doesn't know that, and you're not going to let her know that you know that.
I'm sorry, but if you really want to be moral here, you should still not fuck her. It sounds like you're taking advantage of, if not also somewhat manipulating an emotionally vulnerable person
