If he does Hajj on behalf of his deceased brother, will that be expiation for him?

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 

Secondly: 

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.