[cstreit]

No sage advice here, but...

..don't let her win by resigning. If the company is in your favor (and it sounds like it is), find a champion within the organization, a higher level individual that can coach you through this.

Perhaps they can help you with a well written letter for the case. I don't think the company is obligated to report this to the "authorities" but they do need to show due-diligence in investigating this in case she ever sues.

Obviously now it will be even tougher to fire her unless your company can prove that she was harrasing you by filing the claim, which of course you can't because it was anonymous. Perhaps your subordinates can find out? (better not drag them into it in retrospect). So maybe you can just mothball her.... off in some harmless assignment that keeps her away from the team. Keep her negative attitude away from them.