If a woman requests a divorce from her husband, and he says to her: "If you truly desire divorce, then as you wish," and at that moment she truly desired a divorce, does the divorce take effect in this case?

The phrase "فكما تريدين" (as you wish) is an allusion to divorce; it does not constitute a divorce unless the husband intends it. If he does not intend it, then there is no consequence for him. But if he does intend it, then he has made the divorce conditional on the wife's will. If she explicitly expresses her desire for divorce, then it becomes effective.

If a divorce occurs, the husband may take his wife back before the expiry of her iddah (definition) (waiting period) if it is the first or second divorce. Her iddah ends with her purification from the third menstrual period, or the passing of three months, or the delivery of the child (if pregnant). If the iddah expires, then a new marriage contract is required.

If it is the third divorce, then she becomes unlawful for him and does not become lawful for him again until she marries another husband a marriage of genuine desire.