How does the religiously sanctioned divorce (ṭalāq sharʿī) proceed for a woman who embraced Islam for marriage then apostatized, knowing that the marriage contract was solemnized by a shaykh who has since passed away and was not officially registered?

It is sufficient for a husband who wishes to divorce his wife to utter the divorce pronouncement, such as saying: "You are divorced." Writing is not a condition for the validity of the divorce, nor is the permission of a judge or a marriage officiant required. There is no need to refer back to the person who drafted the marriage contract or to tear up the contract document. However, documenting the divorce is now essential to avoid disputes and conflicts.