All perfect praise be to Allah, the Lord of the worlds. I testify that there is none worthy of worship except Allah and that Muhammad, sallallaahu ‘alayhi wa sallam, is His slave and Messenger.
If this man believes that it is obligatory for women to wear the Niqab, then it is not permissible for him to allow his wife to uncover her face before non-mahram (permanently unmarriageable) men regardless of whether she stipulated this or not. If she stipulated not wearing the Niqab, then the stipulation is invalid because it makes lawful what is unlawful. In this case, we advise him to leave this woman and look for another religious one. However, if he believes that it is permissible for a woman to uncover her face, as is the view of the Maliki and Hanafi scholars, who conditioned that she is not likely to cause temptation by uncovering her face, then it is permissible to marry her and fulfill her stipulation provided that she is a religiously committed woman. He may later encourage her to wear the Niqab by highlighting its virtues to her.
Finally, we also remind you that although there is a difference in opinion on whether the Niqab is obligatory or not, the original ruling is that the wife is obliged to obey her husband when he commands her to wear it.
Allah knows best.