Is it permissible to pray on behalf of an incapacitated mother at certain times?

Prayer does not permit deputization. One who is unable to pray standing should pray sitting. If unable, they should pray on their side. If still unable, they should pray lying on their back with their feet towards the Qiblah, based on the Almighty’s saying: (So fear Allah as much as you are able). As for one whose intellect has been affected by senility or insanity, there is no prayer obligatory upon them, nor can anyone pray on their behalf. The sane, accountable person prays according to their condition.