Is it permissible to perform Hajj on behalf of a deceased relative who never performed Hajj, with the intention of covering the Hajj expenses and then informing his financially capable mother about it later, and is this action valid?

May Allah reward you for your eagerness to benefit your deceased relative through Hajj and charity, and to bring joy to your cousin. This is among the best deeds and a way of upholding kinship ties. As for the expenses of Hajj that you wish to take from the deceased's mother, there is no harm in it for you. However, it is preferable to inform the deceased's mother beforehand of your intention to perform Hajj on behalf of her son and to ask her to donate whatever she wishes. If you take money from her as expenses for Hajj, you must be economical and avoid extravagance. You are obliged to return any remaining money to her, unless she permits you to keep it.