If you can identify the perp, it would seem that you have potential damages if you can quantify and prove monetary losses you experience as a result of the false claim. Small claims court might be an option. Significant damages would warrant hiring an attorney. If you go the small claims route and win, collecting is another issue altogether.
For the most part, you are on your own for collection. It is tedious and time consuming at best. There are a myriad of sites that provide the gruesome details. However, if you do prevail, you can file a judgement against the offending party, and this will appear on their credit rating. This can be devastating to individuals who rely upon good credit. Best case: you acquire, I believe, non-taxable income.