Is it permissible for a woman who has been divorced twice by her husband to return to him after his third divorce of her, and how would this be done, knowing that the first two divorces were verbal and the second by marriage contract?

A husband's pronouncement of divorce upon his wife, whether verbally or documented, counts as a divorce. Neither reconciliation during the waiting period (iddah (definition)) nor renewing the marriage contract prevents that pronouncement from being counted as a divorce. If the pronouncements of divorce reach three, the wife becomes irrevocably divorced (baynunah kubra), and she is not permissible for her first husband until she marries another man willingly, and then he divorces her or dies, based on the Almighty's saying: "Divorce is twice. Then, either keep [her] with acceptance or release [her] with goodness... And if he has divorced her [for the third time], then she is not lawful to him afterward until she marries another husband. And if he [new husband] divorces her, there is no blame upon them if they return to each other and assume that they will maintain the limits of Allah."