First off, if your question is whether this is criminally prosecutable, the answer is that the local authorities make those decisions. Individuals merely file police reports. Specifically, the District Attorney's office, makes the decision to file charges. In this case, I seriously doubt that the DA would ever get involved. The DA has much more serious matters/crimes to chase down than this one. The police are not going to get involved unless the sheriff has to serve a subpeona
If he wants to file a defamation law suit, he can hire an attorney, plunk down a retainer and then the attorney can subpeona the Facebook records, etc for the IP address. Will this actually happen? Who knows? People make lots of threats of this nature, but when it comes time to put money where their mouths are, they often back down. IMO, he is blowing smoke.
In theory, at least, it is possible that she will get sued. She would have been better off doing this one from a public computer, such as one at a library or a place like Kinko's. It probably would be difficult in these circumstances to know exactly who was using any particlar public computer at any given time, especially if she paid in cash (in the case of a place like Kinko's.)