If a menstruating woman purifies herself after the Fajr adhan, and she does not know whether she purified herself before or after Fajr, is she obligated to make up the Maghrib and Isha prayers?

The certainty is that the woman was menstruating, and purity is an emergent state for her. Certainty is not removed by doubt, so she is not required to make up the Maghrib and 'Isha prayers. And if she doubts whether her menstruation stopped before Fajr or after it, she is not required to make up the night prayer until she is certain that it stopped before Fajr.