Is it permissible to perform Hajj on behalf of a mentally and physically disabled sister without her consent, knowing that the one performing Hajj has already fulfilled his own obligatory Hajj?

The questioner is not permitted to perform Hajj on behalf of her sister, even if the sister agrees, because that involves lying and bearing false witness, which are among the greatest major sins warned against by the Prophet, peace and blessings be upon him, when he said: "Shall I not inform you about the greatest of major sins?" And he mentioned among them: "Indeed, false speech, indeed, false witness." If she wishes to perform Hajj again, she must wait for a permissible means.