Hajj on behalf of a deceased father who did not pray
Question

                My father died a long time ago, and I know that he did not pray. I came to Saudi and I have done the obligation of Hajj three times. The last time I intended that it should be on behalf of my deceased father, but I heard of a ruling that a person who does not pray is regarded in sharee’ah as a kaafir, and I was very upset when I thought about my father’s situation. My question is: is this Hajj permissible, and will it expiate for his shortcoming with regard to prayer?.
Praise be to Allah.This question was put to Shaykh Muhammad ibn ‘Uthaymeen (may Allaah have mercy on him) who said: 
This questioner mentions in her question that 
    she had done the obligation of Hajj three times. The correct view is that Hajj is obligatory only once in a lifetime, because it was proven that 
    the Prophet  (peace and blessings of Allaah be upon him) said: “Hajj is once in a lifetime, and any more than that is voluntary.” So your 
    saying that you have done this obligation three times is a mistake. 
With regard to your having done Hajj on 
    behalf of your father who did not pray, the kuffaar do not benefit from righteous deeds, and it is not permissible to seek forgiveness for them, 
    because Allaah says (interpretation of the meaning): 
“It is not (proper) for the Prophet and 
    those who believe to ask Allaah’s forgiveness for the Mushrikoon, even though they be of kin, after it has become clear to them that they are the 
    dwellers of the Fire (because they died in a state of disbelief)”
[al-Tawbah 9:113]
But since your father did pray sometimes, or there is some doubt as to whether he can be 
    regarded as a kaafir, there is nothing wrong with your doing Hajj on his behalf and saying, “O Allaah, give the reward for this to my father if he 
    was a believer.” Connect that to the condition of your father being a believer. There is nothing wrong with that, because making conditions is 
    permissible with regard to matters of worship and du’aa’. 
With regard to acts of worship, the Prophet 
     (peace and blessings of Allaah be upon him) said to Dabaa’ah bint al-Zubayr (may Allaah be pleased with her), when she wanted to do Hajj but 
    she was sick, “Do Hajj and make a condition, because your condition is valid with your Lord.” Narrated by al-Bukhaari, 5089; Muslim, 1207. 
With regard to du’aa’: Allaah says in the 
    verse on li’aan (interpretation of the meaning):
 “And the fifth (testimony should be) the 
    invoking of the Curse of Allaah on him if he be of those who tell a lie (against her)”
[al-Noor 24:7]