Does he have to do ‘umrah if he has money but he needs to complete his studies?

Firstly: 

The correct view is that it is obligatory to do ‘umrah once in one’s lifetime if one is able to do so. 

This has been explained in the answer to question no. 39524 

If you have fulfilled the conditions of it being obligatory (being able to afford it financially and being physically able to do it), then you must do ‘umrah right away, and it is not permissible for you to delay it without an excuse. 

Al-Hajaawi (may Allah have mercy on him) said: Hajj and ‘umrah are obligatory for a Muslim who is free, accountable and able to do them, once in a lifetime, to be done without delay. 

Shaykh Ibn ‘Uthaymeen (may Allah have mercy on him) said: 

The phrase “without delay” means: it is obligatory to do them immediately, once the conditions of it being obligatory are met. 

The evidence for that is as follows: 

(i) The verse in which Allah, may He be exalted, says (interpretation of the meaning): “And Hajj (pilgrimage to Makkah) to the House (Ka‘bah) is a duty that mankind owes to Allah” [Aal ‘Imraan 3:97].

(ii) The hadith of Abu Hurayrah: “O people, Allah has ordained Hajj for you, so perform Hajj.” The basic principle is that a command is to be done immediately, hence the Prophet (blessings and peace of Allah be upon him) got angry during the campaign to al-Hudaybiyah when he instructed the people to exit ihram and the people were slow to respond.

(iii) The individual does not know what will happen to him. He may be able at present to obey the command of Allah, may He be glorified and exalted, but in the future he may be unable to do so.

(iv) Allah has commanded us to hasten towards all that is good, as He says (interpretation of the meaning): “So hasten towards all that is good” [al-Baqarah 2:148]. Delaying is contrary to what Allah has enjoined. This is the right view, that it is obligatory to comply with Allah’s commands immediately. 

End quote from ash-Sharh al-Mumti‘ (7/13) 

Secondly: 

If a person has money but he needs it to buy a house or to get married or complete his studies, then in that case there is nothing wrong with him delaying ‘umrah until he is able to do it, because in this situation he is not regarded as being able to do Hajj and ‘umrah; rather they are obligatory for the one who is able to do them. 

A l-Hajaawi (may Allah have mercy on him) said in Zaad al-Mustaqni‘: 

The one who is able (to do Hajj and ‘umrah) is the one who is able to travel, and has sufficient provisions and means of transportation that are fit for ones such as him, after covering obligatory expenses as prescribed in Islamic teaching and his family’s basic needs. 

The phrase basic needs means that he must have wealth surplus to what is required to meet basic needs, and they are things that people often need, because there are both basic needs and minor needs. 

Basic needs include things like books, pens, a means of transportation, and other things which are not absolutely essential, but people need them. If a seeker of knowledge has books that he needs to refer to and read, we do not tell him: Sell your books and go for Hajj.

End quote from ash-Sharh al-Mumti‘ (7/29)

For more information please see the answer to question no. 11534

And Allah knows best.