Is it permissible to perform Hajj al-Badal on behalf of a Muslim who has lost his memory and is not expected to recover?

It is permissible to perform Hajj on behalf of a Muslim who has lost his memory or is insane, specifically for supererogatory Hajj (Hajj al-Tatāwwo‘) and not for the obligatory Hajj (Hajj al-Farīḍah). This is due to the possibility that the person who lost his memory might regain it, or the insane person might recover. However, if two trustworthy doctors conclusively state that the recovery of memory is hopeless, then the obligatory Hajj may be performed on his behalf. As for someone who reached puberty while insane, Hajj is not obligatory upon him. Nevertheless, if someone else performs Hajj on his behalf, it is permissible, and the performer will be rewarded for it.