Is it permissible for a sister to pay money on behalf of her sister who was unable to fast Ramadan due to her inability to fast, and wishes to pay fidyah in money instead of feeding the poor?

If a trustworthy doctor informs you of your inability to fast and make up for missed fasts, an inability that is not expected to cease, then you are excused. It suffices for you to pay a fidyah (expiatory feeding) for each day of Ramadan. Its amount is approximately 750 grams of the staple food of your country, and it should be given to the poor and needy. If your sister or someone else volunteers to pay the fidyah on your behalf, that is sufficient.