Is it permissible for a menstruating woman to fast Ramadan out of modesty, on the condition that she makes up the days after the month, without actual prayer or fasting?

A menstruating woman must break her fast, and it is forbidden for her to fast during her menses. If she fasts, that fast is not valid for her, and she must make up for it after she becomes pure. She may eat and drink away from the sight of those who are fasting, and it is not permissible for her to fast out of reverence for the month.