Is it permissible for him to send his mother for Hajj using the zakaah of his wealth?
Question

                I am comfortably off and I have decided to send my mother for Hajj. Is it permissible for me to regard the money that I will send for her to use on the expenses of Hajj as the zakaah of my wealth? In other words: is it one of the categories on which zakaah is to be spent to use it to help my mother to perform the obligation of Hajj?.
Praise be to Allah.
    Firstly: 

    If your mother does not have the money to do Hajj, then Hajj 
    is not obligatory in her case, because Allah, may He be glorified and 
    exalted, says (interpretation of the meaning):

    “And Hajj (pilgrimage to Makkah) to the House (Ka'bah) is 
    a duty that mankind owes to Allâh, those who can afford the expenses (for 
    one's conveyance, provision and residence)”

    [Aal ‘Imraan 3:97]. 

    If the son wants to send his mother for Hajj, the scholars 
    differed as to whether it is permissible to pay for that from zakaah. The 
    reason for this difference of opinion is that Allah listed, among the 
    categories on which zakaah may be spent, “and for Allâh's Cause” 
    [al-Tawbah 9:60]. Does this include Hajj or does it apply only to jihad 
    for Allah's cause? 

    Most of the scholars are of the view that Hajj is not 
    included in the categories on which zakaah may be spent. 

    Ibn Muflih al-Hanbali (may Allah have mercy on him) said: 

    It (zakaah) cannot be given for Hajj. According to one 
    report, he favoured this view in al-Mughni and classed it as sound in
    al-Sharh. This was also stated by most of the scholars, because the 
    phrase “Allah’s cause (sabeel-Allah) usually refers to jihad, and zakaah is 
    only given to those who need it, such as the poor, or those whom the Muslims 
    need, such as the worker who collects and distributes zakaah. The Muslims do 
    not benefit from one individual’s Hajj and have no need for it; it is not 
    obligatory in the case of the poor, for whom this duty is waived, and if a 
    poor person still wants to do it, it is better to spend this amount of money 
    on those who are in need or to spend it on helping the Muslims. 

    Al-Mubdi‘ Sharh al-Muqni‘, 
    2/387 

    Imam Ahmad has another view, which is that it is permissible 
    to give zakaah to someone who wants to do Hajj. This view was also favoured 
    by Shaykh al-Islam Ibn Taymiyah (may Allah have mercy on him), and is 
    mentioned in fatwas issued by the scholars of the Standing Committee for 
    Issuing Fatwas. 

    This has been discussed previously in the answer to question 
    no. 40023. 

    Based on this second opinion, it is permissible for you to 
    send your mother for Hajj using the zakaah of your wealth. But if you take 
    the more cautious approach and do not regard this as zakaah, that is 
    preferable, and we hope that Allah will accept it from you and from her. 

    And Allah knows best.