My sister is disabled. She is 14 years old. She is not able to move and can only speaks through gestures. My mother provides a charity on her behalf for every day of Ramadan. Is this valid?

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 sister is mentally sound and has reached puberty – signs like menses, sexual discharge, or pubic hair have appeared – and her disability does not hinder her from fasting but trustworthy doctors declare her totally and chronically unable to fast, then she is required to offer the respective expiation instead of fasting. The expiation remains a debt on her if she cannot afford it at the moment. In Al-Mughni, Al-Khateeb Al-Shirbeeni said:

If a Muslim fails to fulfill a financial obligation in its due time, then such an obligation becomes a debt that he remains liable to. This applies even if the respective financial obligation is not prescribed as a substitute for something else and is caused by the Muslim himself. This is the case here since the expiation is caused by the Muslim’s fast-breaking.

It is acceptable that your mother offers the expiation on behalf of your sister, regardless whether your sister is poor or rich.  

However, if doctors decide that your sister will be able to fast after receiving treatment, then it is not permissible to offer the expiation. Rather she then has to wait until she becomes able to fast and then make up for the days that she has missed. Allaah, the Exalted, says (what means), {Then an equal number of days [are to be made up].} [Quran 2: 184]   

Allaah Knows best.