Is it permissible for an elderly, ill mother who has difficulty moving and performs tayammum by striking her palm on the wall for prayer, to pray with this tayammum?

Among the acts of filial piety towards an elderly mother is assisting her with ablution (wudu') with water. If she is unable to do so, they should help her perform tayammum (dry ablution), for example, by bringing her earth in a container. As for performing tayammum on a wall, it is permissible according to the Malikis and Hanafis if the wall is made of earthy material. If the wall is not made of earthy material, or if she cannot find anything to perform tayammum with, then she should pray in her current state due to her inability, and she does not have to repeat the prayers she performed without water or earth, for Allah Almighty says: "So fear Allah as much as you are able."