Must One Censure a Man Who Has Divorced Yet Still Resides with His Divorcee?

Answer—and Allah is the One who grants success: What appears—and Allah knows best—is that you must alert him to his error, explain divorce and its rulings, admonish and warn him. Nothing further is incumbent upon you.
It is not permissible to categorically declare him an open sinner (fāsiq). There are possibilities that open the door to interpretation: divorce is of the Sunnah and of innovation; some scholars have said the innovated does not take effect. Perhaps this man’s “three” were in a single phrase; or one of the three was during his wife’s menstruation, or during a purity in which he had cohabited with her. On such grounds, his divorce would not take effect according to some scholars. They have said: “The madhhab of the pure layman is the madhhab of whomever he accords with.”
And in al-Muhadhdhab by Imām al-Manṣūr Billāh (peace be upon him): “If one acknowledges that he divorced his wife three times, then retracts his acknowledgment: if she does not dispute with him and he claims he was mistaken, or he adduces a proof whose occurrence is plausible, and the woman does not dispute him before his retraction—then it is permissible for him to cohabit with her privately between him and Allah Most High.”
And in the marginalia upon al-Muhadhdhab: “This is like what our companions said about one who said to his wife, ‘You are divorced,’ then claimed he intended by it other than its apparent meaning, and the woman did not dispute him: the Muslims are not obliged to denounce him, nor to bring him before the judge.” End.
Source : Min Thimār al-ʿIlm wa al-Ḥikmah vol.1