Sounds very frustrating.
You have done everything that would be required or expected of you and your husband upon learning of the fraud. I assume from your question you would like to find out the identity of the individual who is fraudulently claiming benefits in the name of your husband. About the only suggestion I could make at this point would be to put a letter together and entitle it "public records request". Put your husband's name and other identifying information in the subject line. Request all documents pertaining to any application for unemployment benefits or the payment of unemployment does benefits. it's a long shot, but you may receive some clue. Finally, be prepared as you may receive no response or further stonewalling.