Please have at least one visit with an attorney to find out what your rights are and what would likely be decided IF you went to court. NOT suggesting you go to court, but knowing that info gives you a better basis for negotiating, and protects you from inadvertently giving away what should be yours.
Maybe he's just anxious to be done, but it's also probable he wants you to lie about the timing in order to "prove" to OW he hadn't lied about separation or something. Don't let H pressure you into lying. (Could OW be pregnant, btw???).
