There is nothing wrong as far as Islamic Shari`ah is concerned in performing Hajj tamattu` or any other type of Hajj on behalf of a deceased family member. However, the only condition is that the person going on other’s behalf should have performed Hajj on their own before performing it on behalf of a relative. So, if this is the case, there is nothing wrong in performing Hajj on behalf of a deceased relative.

Allah Almighty knows best.