Is it permissible for a woman whose husband divorced her three times, and did not give her a divorce certificate, to enter into an 'urfi marriage after her 'iddah has expired?

If a man divorces his wife with three pronouncements, she becomes irrevocably separated from him (baynunah kubra). She does not become lawful for him again until she marries another man with a valid marriage that fulfills all conditions (such as the guardian and witnesses). The fact that the marriage is " عرفيًا " (customary/unregistered) does not affect its validity. The non-documentation of divorce or marriage does not prevent their occurrence or validity. However, documentation is essential for safeguarding rights and resolving disputes. This falls under the category of "masalih mursalah" (undetermined public interests) that achieve the objectives of Islamic law in bringing about benefits and averting harms.