Is the third divorce (ṭalāq) for a woman divorced twice considered a valid divorce according to Sharia, and does the divorce of a divorced woman take effect, and is it permissible to take her back (rajʿa)?

If a man divorces his wife twice and does not take her back until her iddah (waiting period) expires, she becomes irrevocably separated from him. If he divorces her after this separation, his divorce is not effective. He may, however, marry her again with a new aqd (marriage contract), and she returns to him, with one divorce remaining for him. Thus, if a divorced woman becomes separated and then her former husband marries her again, and then divorces her fewer than three times, and she returns to him before marrying another husband, she returns to him with the remaining divorces.