Answer
Wa `alaykum as-Salamu wa Rahmatullahi wa Barakatuh.
In the Name of Allah, Most Gracious, Most Merciful.
All praise and thanks are due to Allah, and peace and blessings be upon His Messenger.
In this fatwa:
It is very kind on your part to pay or feed poor people on behalf of your grandmother who is not able to fast. By doing so, you will gain two rewards, one for helping your grandmother paying or feeding for her missed fasts and the second for fostering ties of kinship. So, it is absolutely permissible to do that.
In his response to your question, Sheikh Ahmad Kutty, a senior lecturer and Islamic scholar at the Islamic Institute of Toronto, Ontario, Canada, states:
It is perfectly OK for you to do so. I would go even further to state that, if you were to do so, it will be reckoned as a great act of kindness on your part to offer money or food to the poor on behalf of your grandmother.
By making the intention that you are paying them in lieu of your grandmother’s missed fasts, she will not only be absolved of her duty to pay, but also will receive the full blessings.
Furthermore, you also stand to gain blessings and rewards for your gesture of kindness on behalf of your grandmother. It is worth remembering that fostering ties of kinship is a supreme act of virtue meriting tremendous rewards.
So go ahead and pay the amount of fidyah (regulated ransom for not fasting) on behalf of your grandmother, if she is poor and therefore unable to pay for herself.
Allah Almighty knows best.
Editor’s note: This fatwa is from Ask the Scholar’s archive and was originally published at an earlier date.