وعليكم السلام ورحمة الله وبركاته It is permissible for you to start fasting the six fasts of Shawwal before making up for what you missed from the fasts of Ramadan. This is the correct one from the sayings of the scholars and it is the opinion of the majority of scholars because it was reported on the authority of Aisha رضي الله عنها that she used to make up what she missed in Ramadan during the month of Sha’ban . This means if she was going to fast in the month of Shawwal it would have been before making up her missed fasts and that was during the lifetime of the Prophet صلى الله عليه وسلم and he did not prevent her from it . Also if you first make up the missed fasts of Ramadan before you start fasting the six days of Shawwal then it is better for you since you will be out of the scholarly disagreement but it is not obligatory on you. Also one of the reasons to support what we mentioned above is that if a woman was in her postpartum period throughout the month of Ramadan and became pure a day before its end and we obliged her to make up the missed fasts before fasting the six days of Shawwal, the result would be that she is prevented from fasting the six days . This kind of view is hard and heavy on them without clear authentic evidence . And if the contrary opinion was true , then the Prophet صلى الله عليه وسلم would have told us about it , because it is something that happens a lot in women. And Allah عز وجل knows best .