Wa `alaykum As-Salamu waRahmatullahi 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.
Dear questioner, we would like to thank you for the great confidence you place in us, and we implore Allah Almighty to help us serve His cause and render our work for His Sake.
Answering your question, Sheikh Ahmad Kutty, a senior lecturer and an Islamic Scholar at the Islamic Institute of Toronto, Ontario, Canada, states:
If your mother was unable to fast because of her health challenges, and she did not pay the fidyah while having the ability to do so, then it is a debt she is owing to Allah. As her daughter, it is your duty – provided you have the means – to offer fidyah on her behalf.
We have traditions from the Prophet (peace be upon him) stating that one may fast on behalf of the deceased parents or pay fidyah on their behalf. The latter is the case if the deceased were too sick to fast because of their old age or terminal sickness. If, however, they were physically able to fast and yet did not fast, then fasting on their behalf is better.
Here are some traditions to support this ruling:
“Whoever dies while failing to fast the required days let his or her heir fast on his or her behalf.” (Al-Bukhari)
A person asked the Prophet (peace be upon him): “My mother passed away while failing to fast the entire month (of Ramadan). Shall I fast on her behalf? The Prophet (peace be upon him): “Yes, because the debt one owes to Allah is more worthy of repayment.” (Muslim)
Based on this, most of the scholars agree that a deceased person’s heirs can fast or offer fidyah on behalf of their parents who have died if they did not observe the obligatory fasts.
Now coming to the issue of fidyah, it is estimated to be a full meal or its cost. So, you are allowed to pay the fidyah in cash. You should consider the cost of a full meal in your country or town and pay accordingly. You may pay more if you wish to; that would be even better if your standard of living is higher than the average person in the city or country as Imam Ibn Taymiyyah has ruled.
Allah Almighty knows best.