Reference: Liqaa.aat al-Baab al-Maftooh – Volume 1, Page 45, Number 67
Question: I have a paralytic son, and am thinking about him doing hajj, because if he was to do the hajj himself, then I fear that he will suffer harm. So is it permissible for me to do the hajj on his behalf?
Response: If the son is [indeed] paralytic as you say, then it is permissible for you to do the obligatory hajj on his behalf if you have already done the hajj for yourself.