He wants to do Hajj first and his father wants him to get married first

Firstly: 

Hajj is obligatory and should be done at the earliest opportunity according to the more correct of the two scholarly opinions. This has been discussed in the answer to question no. 41702. 

If the available money is sufficient for either doing Hajj or getting married, then precedence should be given to marriage if there is a need for that and there is the fear of falling into haraam. If there is no (urgent) need for marriage, then Hajj should be given precedence. 

Ibn Qudaamah (may Allah have mercy on him) said in al-Mughni (5/12): If (the individual) needs to get married and fears that he may encounter hardship, then he should give precedence to marriage, because it is obligatory in his case and he cannot do without it, so it is like spending on his maintenance. If there is no such fear, he should give precedence to Hajj, because marriage is voluntary and should not be given precedence over the obligatory Hajj. End quote. 

Shaykh Ibn ‘Uthaymeen (may Allah have mercy on him) was asked: Is it permissible to delay Hajj until after getting married for one who is able to do it? That is because of what the youth are facing nowadays of temptation, both great and small. 

He replied: 

There is no doubt that marriage, for one who has the desire and urgent need for it, takes precedence over Hajj, because if an individual has overwhelming desire, in that case marriage becomes one of the necessities of life, like eating and drinking. Hence it is permissible for one who needs to get married and does not have any money to be given zakaah funds with which to get married, just as the poor person may be given food to suffice him and clothes with which to cover his ‘awrah out of the zakaah funds. 

Based on that, we say: if he needs to get married, then he should give marriage precedence over Hajj, because Allah, may He be glorified and exalted, stipulated that in order for Hajj to be obligatory, one must be able to do it, as He says (interpretation of the meaning):

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

[Aal ‘Imraan 3:97].

In the case of one who is young and it does not matter for him whether he gets married this year or next year, then he should give precedence to Hajj because it is not necessary for him to give precedence to marriage.

End quote from Fataawa Manaar al-Islam, 2/375 

Based on that, if you do not have any fears (of falling into haraam) if you delay marriage, then you should hasten to do Hajj first, and Allah will compensate you with good, because Hajj is one of the important obligatory duties and rituals of Islam. 

You do not have to carry out your father’s wishes with regard to this matter, either during his lifetime or after his death, because that would result in your delaying Hajj when there is no need to do so. 

Secondly: 

You should have tried to please your father by giving precedence to marriage over completing your postgraduate studies. It was narrated from Imam Ahmad (may Allah have mercy on him) that marriage is obligatory if either of the parents tell you to get married. 

Al-Mirdaawi said: Is it (marriage) obligatory if the parents, or one of them, tell the son to get married? Imam Ahmad (may Allah have mercy on him) said: If he has parents who are telling him to get married, then I tell him to get married. Or if he is a young man who fears that he may commit sin, I tell him to get married. 

By saying this, he made the parents’ instructions to get married equivalent to fearing that one may commit sin.

End quote from al-Insaaf, 8/14 

Thirdly: 

There is nothing wrong with a father doing Hajj with his son’s wealth; in fact there is nothing wrong with a person doing Hajj with another person’s wealth in general. But if a person was not able to do the obligatory Hajj because he could not afford the expenses, then he became able to afford it if someone else pays for it, does he have to accept this money in order to do Hajj? There is a difference of opinion among the fuqaha’ concerning that. 

Ibn Qudaamah (may Allah have mercy on him) said: He is not obliged to do Hajj if someone else spends on it, and he does not become able to do it thereby (and thus it does not become obligatory for him), whether the one who gives him the money is a relative or otherwise, and whether he gives him a means of transportation and provisions, or he gives him money. However, it was narrated from ash-Shaafa‘i that if a person’s son gives him money that enables him to do Hajj, then he is obliged to do it, because he has enabled him to do Hajj without feeling that he owes a favour to anyone, and no harm or annoyance will result from that. Therefore he is obliged to do Hajj, as would be the case if he possessed sufficient provisions and a mount. 

In our view, the words of the Prophet (blessings and peace of Allah be upon him) make Hajj binding on one who has a means of transportation and sufficient funds to cover the costs of the journey. However, in the case where someone else offers to over these costs, he is not regarded as having the means or the money to obtain the means, so Hajj is not obligatory for him. The same applies if his father offers to help him, because we do not think that the father will not feel that he owes him a favour in this case. 

End quote from al-Mughni, 3/87 

To sum up: it is obligatory for you to hasten to do Hajj, so long as you do not think that you will fall into haraam as a result of delaying marriage, and you should ask Allah, may He be exalted, for forgiveness for having gone against your father’s instructions when he told you to get married first. 

We ask Allah to help and guide you. 

And Allah knows best.