Q: What is the ruling regarding
a woman who fasts two days that she missed of Ramadan without her husband's permission
i.e. without telling him. She felt shy to tell her husband. If it was not permissible for her to do this, should she expiate (offer Kaffarah) for it?
A woman has to make up for the days that she did not fast in Ramadan even if it is without her husband’s knowledge. For obligatory Sawm (fast), her husband’s permission is not necessary. So the Sawm of the woman mentioned is valid. As for non-obligatory Sawm, a woman should not offer Sawm while her husband is present except with his permission, because the Prophet (peace be upon him)
forbade that a woman should fast, at any time other than Ramadan, while her husband is present without his permission.
May Allah grant us success. May peace and blessings be upon our Prophet Muhammad, his family, and Companions.