وعلیکم السلام ورحمتہ اللہ وبرکاتہ
Shafi’i scholars are of the opinion that whoever fasts the missed days of Ramadan simultaneously with the six days of Shawwal have fulfilled their religious obligation as well as obtained the reward for fasting the six days from Shawwal. However, one should not intend to fast the six days of Shawwal but should intend only to make up what one has missed from Ramadan. And since these make up days will fall during Shawwal, one will obtain the reward of the sunnah fast as well. Indeed the generosity of Allah SWT is vast. This opinion is based on the hadith of the Prophet (peace and blessings be upon him) who said: “Whoever fasts Ramadan and follows it with six days from the month of Shawwal, it is as if he has fasted the entire year.” The Prophet (peace and blessings be upon him) did not mention that one should make an intention to fast these six days; rather his words were general in that they should follow the month of Ramadan. These six days can be achieved by intending to make a sunnah fast or to make up the missed fast days of Ramadan.
Imam Al-Ramli issued a fatwa that agrees with this this position. He said that a person who makes up the missed days from Ramadan in Shawwal, even if he intends other than the fast of Shawwal, obtains the reward for the six days of Shawwal.
Based on this, it is permissible for a woman to make up her missed fast days of Ramadan during the month of Shawwal and obtain the reward for fasting six days of Shawwal.
Stay blessed.