Is the Hajj that the questioner intends to perform on behalf of his deceased father, who did not pray during his lifetime, beneficial to him? And if it is not beneficial to him, then what does the questioner advise the questioner to do with the remaining money?

What is given to the deceased's family as aid for burial expenses and similar costs, any remainder should be disposed of according to the donor's specifications, or else by custom and common practice. This money is not exclusive to any one member of the deceased's family to dispose of as they wish, nor is the questioner permitted to dispose of it alone. Because if its uses are not specified by the donor and there is no custom, then it is considered a joint gift among the deceased's family. No individual among them has the right to dispose of it except for their own share after division. As for performing Hajj or any good deed on behalf of someone who abandoned prayer, that has a different ruling.