Is it permissible for a daughter to make up the Ramadan fasts on behalf of her deceased father, who broke his fast due to cancer and was unable to make up the days or feed the poor, and is it obligatory only for sons to fast on his behalf, or is it also permissible for daughters?

Fasting on behalf of the deceased is not obligatory for their heir or guardian. As for the sick person from whom recovery is not expected, their obligation is to feed, not to fast. If they die without having fed, their guardian must feed on their behalf from their estate, as an obligation. It is recommended to do so even if they left no estate. Fasting on their behalf is not legislated and is not valid at all, for Ibn 'Uthaymeen said: "Indeed, your father is not obliged to fast as long as his illness is not expected to recover. Therefore, what is obligatory is that he feed a poor person for each day, and you should not fast on his behalf." The hadith "Whoever dies while owing fasts, their guardian should fast on their behalf" applies specifically to one who was able to make up the fasts but did not do so.