I wish that you answer my question. My mother is afflicted with a chronic illness and a Muslim physician has advised her not to fast. Is it permissible for me, her daughter, to observe the missed Ramadhaan fasts that must be made up on behalf of her on other days or is it necessary to expiate by giving food to indigent people? And how much should the expiation be?

All perfect praise be to Allaah, the Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad, sallallaahu ‘alayhi wa sallam, is His Slave and Messenger.

If your mother will be permanently unable to make up for the missed fasts, then expiation is due on her, which is to give food to an indigent for each missed fast. The amount of food for expiation is approximately 750 grams of the most common foodstuff in your country - to be given to one indigent for each missed fast. It should be known that fasting on behalf of her will not fulfill the obligation. 

Allaah Knows best.