Is it permissible to conclude a secret or customary marriage contract to legitimize the relationship between a man and a divorced woman, knowing that her divorce has not yet been documented, and she refuses to sue her ex-husband for divorce, and is currently unable to move in with him?

You are Islamically permitted to marry a divorced woman even if she has not obtained the official divorce document. Divorce, according to Islamic law, takes effect the moment it is pronounced by the husband, and her waiting period (iddah) begins from the date of the divorce's pronouncement, not its documentation. If her waiting period has ended, she is permitted to marry whomever she wishes. For a valid Islamic marriage to be complete, its conditions must be met, including the presence of a guardian (wali) and two witnesses. There is no harm in not immediately documenting the marriage or delaying its public announcement. Any illicit relationship with the woman must be rectified, either by marriage or by terminating it, while it is permissible to assist her if she is in need.