What is the ruling on a judge divorcing a wife based on false testimonies and claims, and is it permissible for her to marry another man?

If the ruling for divorcing your wife was issued based on false testimony, and you did not pronounce the divorce yourself, then the judge’s ruling is religiously invalid, and your wife is still under your marital bond. However, for her to return to you, it is necessary to nullify the divorce ruling issued by the court, or to formalize a new marriage contract to avoid harm and loss of rights.