He agreed with his father that he would pay the Hajj expenses for his mother, then his father died before he could take her
If there was an agreement between you and your father that he would take your mother for Hajj and you would pay him the expenses of Hajj, and he did that, then the expenses are a debt that you owe to your father and should be added to his estate like the rest of his wealth and any debt that was owed to him by other people, and the estate should be divided among all the heirs, of whom you are one.
Including debts that are owed to the deceased by others with the estate is something on which the fuqaha’ are unanimously agreed.
See: al-Mawsoo‘ah al-Fiqhiyyah, 11/208
Based on that, these expenses should be worked out and divided among the heirs, with each heir taking the share allotted to him according to sharee‘ah.
And Allah knows best.