Sheikh Fawzān (may Allāh preserve him) said:

Whoever has had an arm or leg amputated is to wash whatever remains of that limb. If his arm has been amputated from the elbow joint, he washes the stump of the upper arm. If his leg has been amputated from the ankle, he washes the stump of the shin. This is because Allāh, Exalted is He, says (the meaning of which translates as), “So fear Allāh as much as you are able” and because the Prophet (May Allāh praise him and Peace be upon him) said, “When I order you to do something, fulfill it as much as you are able” [reported by Bukhārī (7288)]. So, if he washes what remains of the parts that have to be washed, he has feared Allāh as much as he is able. [Page 34 of Sheikh Fawzān ’s Al Mulakhkhaṣ Al Fiqhī (Summary of Islamic Jurisprudence) (Arabic version)].