Is it permissible for a woman to fast six days of Shawwal for herself, and six days for her deceased mother, and six days for her deceased father, knowing that her parents did not fast Shawwal?

The fact that my parents, may God have mercy on them, did not fast these days does not affect the matter, as long as they were Muslims. There is no evidence that the deceased benefits only from acts of worship that they themselves used to perform. The virtue of fasting six days of Shawwal is conditional upon having fasted Ramadan beforehand, which is not possible for the deceased. Therefore, fasting these days on behalf of the deceased is no more than fasting any other days of the year.