Praise be to Allah.
The saheeh evidence indicates that Hajj is very important and that it expiates sins, and that the one who does it goes back (free of sin) as on the day his mother bore him. But does that include both major and minor sins, or only minor sins? There is a difference of scholarly opinion concerning that; the majority of scholars are of the view that Hajj only expiates minor sins and that in the case of major sins, it is essential to repent from them specifically. Please see the answer to question no. 34359
It is permissible for an individual to perform Hajj on behalf of his brother who has died and did not perform the obligatory Hajj for himself, and the reward for the Hajj will go to the one on whose behalf it was performed. The one who performs the Hajj will have a similar reward, according to some scholars, such as the one who said that he will have a great reward, but it will not be like the reward of the one on whose behalf Hajj was performed. See the answer to question no. 111407 and 111794
Undoubtedly Hajj on behalf of another is regarded as an act of kindness and upholding ties of kinship, hence it is hoped that the one who does it will have a great reward. “Is there any reward for good other than good?” [ar-Rahmaan 55:60].
As the reward of the Hajj will go to the deceased, there is the hope that it will be expiation for his sins, for Allah’s grace is immense and His mercy encompasses all things.
We ask Allah to help and guide you.
And Allah knows best.