All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger.
It is desirable for a Muslim to perform Hajj and ‘Umrah on behalf of his parents who died and who were not able to perform Hajj as the Prophet ordered Abu Razeen to do so, telling him: "Perform Hajj and ‘Umrah on behalf of your father.” [At-Tirmithi] This is already clarified in Fataawa 84509 and 84653.
However, it is more appropriate to start with the mother because Allaah mentioned her when advising the children to be kind to their parents, and the Prophet gave her more right to the kindness of the children when a man asked him saying: “Who deserves my good company more?”, and he replied: “Your mother.” The man asked: “Then who?” The Prophet said: “Then your mother.” The man asked again: “Then who?” The Prophet again replied: “Then your mother.” The man asked again: “Then who?” Thereupon, the Prophet said: “Then your father.” [Al-Bukhari and Muslim]
As-San’aani said in “Subul As-Salaam” when commenting on this Hadeeth: “This implies favoring the mother in kindness and dutifulness and that she deserves them [kindness and dutifulness] more than the father.”
Besides, Ash-Shawkaani said in “Nayl Al-Awtaar”: “This is evidence that the mother deserves more good companionship than the father and that she deserves more kindness and dutifulness of the children than him.”
In any case, if the son performs Hajj or ‘Umrah on behalf of his parents, this will benefit them and the reward will reach them, Allaah willing. For more benefit, please refer to Fatwa 86715.
Allaah Knows best.