What is the legitimate Islamic solution for this complex problem that involves a fake divorce, forgery of a marriage contract, and bringing a girl into the country as a legitimate wife, which resulted in psychological harm to both parties?

If a husband obtains a divorce certificate or a marriage certificate without uttering the words (of divorce/marriage) or forming the intention, then the divorce is not effective and the marriage is not عقد (contracted). His action is objectionable and a forbidden stratagem. The husband is advised to present his case to the Sharia court or to the scholars at the Islamic center, so they may guide him to the correct course of action.