All perfect praise be to Allaah, the Lord of the worlds. I testify that there is none worthy of worship except Allaah and that Muhammad, sallallaahu ‘alayhi wa sallam, is His slave and Messenger.
The majority of the scholars are of the opinion that Hajj is obligatory on an immediate basis. If the person delays it after having had the ability to perform it, then he is deemed guilty for that delay. Thus, your mother is required to immediately perform Hajj as long as the following prerequisites are fulfilled:
- She has enough money – more than what is necessary for her expenses as well as the expenses of those whom she is responsible to spend on until she comes back from the journey of Hajj.
- She is physically able.
- The road is safe.
- She has her husband or a Mahram (permanently unmarriageable) man to accompany her during the journey for Hajj. If this is not available but she has a trusted group to travel with, then she can do so.
Paying the costs of your study is not a sound excuse to allow her to delay Hajj. Such expenses are not part of the maintenance which the father is commanded to provide for his children under the Sharee'ah, then the mother, with greater reason, is not obliged to do provide it.
So we advise the mother to hasten to perform Hajj, in compliance with the Hadeeth in which the Prophet, sallallaahu ‘alayhi wa sallam, said, "Whoever wants to go for Hajj, let him hasten to do it, because he may fall ill or lose his riding animal, or an excuse may arise to him." [Ahmad and Ibn Maajah; Al-Albani: good]
Allaah Knows best.