Is it permissible to pay the fidyah for a mother who is ill with a stroke and hemiplegia, by feeding one needy person for each day, and can the entire amount be paid at once to a charitable organization, and is it permissible to delay the expiation until after the month of Ramadan?

If your mother is unable to fast due to illness, and there is hope for her recovery, then she must make up the missed fasts when she recovers, and she is not required to feed the poor.

However, if doctors have determined that her illness is chronic and there is no hope for recovery, then she must feed one poor person for each day of Ramadan (definition). She may collect all the feeding (fidya) and distribute it after the end of the month, or she may feed one poor person for each day on its own day. She is not permitted to feed for a day before its time has begun.