I say, and with God's help: If the fasting is due to a legitimate excuse such as menstruation, it is permissible for a woman to fast the six days of Shawwal first, and then make up the days she missed in Ramadan. This is because making up the missed days is an obligation that can be fulfilled until the next Ramadan, and the reward is based on fasting the number of days of the month plus the six days, not on the fact that Shawwal comes after completing Ramadan. And God knows best.