Does a wife remain her husband's wife after obtaining a judicial khulʿ without his consent or approval, and can she marry another man?

Khul‘ does not require the pronouncement of divorce. It is an annulment, not a divorce, and by it, the wife becomes irrevocably separated (baynunah sughra). The husband does not have the right to take her back except with a new contract. This is in exchange for financial compensation. The judge may compel the husband to divorce or to khul‘ if there is a reason to do so. If the khul‘ or divorce is executed through the court, the husband has no recourse but to approach the court and try to persuade it to reverse its decision, or to obtain an official fatwa declaring the khul‘ invalid and submit it to the court.