Is it permissible to perform tayammum after every prayer for someone who finds it difficult and arduous to perform ghusl and wudu due to the amputation of both feet, or is ghusl and wudu obligatory upon him?

Abandoning prayer is one of the gravest sins; it is the pillar of the religion. A Muslim must perform the prayer as long as their mind is sound. A Muslim performs what they are able to of the conditions and pillars of prayer, and what they are unable to perform is waived. If one is in a state of major ritual impurity (janābah) and is unable to perform ghusl, they wash what they can and wipe over what they are unable to wash. If they are unable to wipe, they perform tayammum. The same applies to wudu': they perform wudu' as much as they are able, wipe over what they are unable to wash, or else perform tayammum for what they are unable to perform.