You can argue its a false report, but dont expect a charge unless there is more than your word vs hers. You can sue her, but does she have lots of money. If so, an attorney would do it on contingency. Otherwise, you will pay hourly on a case not worth your time and money. You dont need to wait to sue her though.
Can he sue? Sure he can. Can he get a judgment against her? Sure he can. Can he get actual money from her as a result of this? Unless she is a Kardashian girl, I doubt it. You are wasting your time with this. You are never likely going to collect 5 dollars from this woman. My advice would be to beat the case in criminal court, and then get a restraining order on this woman - she sounds crazy. Then you need to have a chat (assuming you have not done so already) that your BF needs to treat her like she is dead and move on and never talk to her or see her ever again.
Boyfriend should hire an experienced criminal defense attorney to investigate this case and present his findings to the DA's Office and seek a refusal to accept the case for prosecution. If already accepted for filing, he or she should seek a dismissal of the case. Then, after two years, he should file a Petition for Expunction to clear his record of this arrest. If boyfriend files a civil suit, he may have his deposition taken, which could give the DA's Office some free discovery in their criminal case. If the DA's Office dismisses, they will decide whether to file false report charges on the complainant.
This would be a civil cause of action (although not likely defamation) and he would need to consult a civil attorney to evaluate the likelihood of winning on such a claim. He will need to expect to spend quite a bit of money (much more than he has already spent) on the civil case. I would typically recommend waiting until the criminal case is disposed of but would defer to whatever his civil counsel recommended. Even if he is found not guilty at trial or the DA dismisses the charges because they refuse to sponsor her testimony (which very rarely happens), it would be up the State to decide whether to turn around and file charges on her. I have personally never seen it happen, and I have handled hundreds of assault cases over then last 10 years.
Macy Jaggers's answer to a legal question on Avvo does not establish an attorney-client relationship. Please consult an attorney who practices criminal law in your jurisdiction for the most accurate legal advice.