Should I fast the days I missed in Ramadan after an illness, due to which I can no longer recall the exact number of days I missed, or is feeding a needy person for the days I fasted sufficient?

The sister must make up what will absolve her responsibility. If she is unsure whether it was three or four days of fasting, she must err on the side of caution and assume the lesser number (three days), because the default is not having fasted, and her responsibility is not absolved except by certainty. It is not permissible to feed the poor as long as she is able to fast. If she delays making up the fast until the next Ramadan begins, she must offer expiation along with making up the fast. If the illness persists, she is not required to make up the fast as long as she is ill, and feeding the poor is not permissible unless her recovery from the illness is not expected.