He is not going to be transferred, so should he take the relocation costs?

It is not permissible for you to take the relocation costs when you are not going to relocate. What you have to do is to leave that money alone and not collect it. You also have to tell the people in charge that you are not entitled to this money. Perhaps by doing that you will set a good example to your colleagues. 

Strive to ensure your food is good [from halaal sources], for Allaah has enjoined upon the believers that which He has enjoined upon the Messengers, which is to eat of good [halaal] things and to do righteous deeds. Allaah says (interpretation of the meaning): 

“O (you) Messengers! Eat of the Tayyibaat [all kinds of Halaal (lawful) foods which Allaah has made lawful (meat of slaughtered eatable animals, milk products, fats, vegetables, fruits)] and do righteous deeds. Verily, I am Well-Acquainted with what you do”

[al-Mumin’oon 23:51] 

“O you who believe (in the Oneness of Allaah — Islamic Monotheism)! Eat of the lawful things that We have provided you with, and be grateful to Allaah, if it is indeed He Whom you worship”

[al-Baqarah 2:172]

And the Prophet SAWS (peace and blessings of Allaah be upon him) said: “Every body that is nourished from haraam sources, the Fire is more suited to it.” Narrated by al-Tabaraani and classed as saheeh by al-Albaani in Saheeh al-Jaami’. 

And Shaykh Ibn Baaz (may Allaah have mercy on him) was asked: I am an employee   working in a government department, and sometimes we are paid overtime by the administration, without us been asked to do any overtime and without us coming to work. They regard it as an occasional bonus for the employees, and the boss knows about that and approves of it. Is it permissible to take this money? If it is not permissible, then what should I do about the money that I have taken previously, noting that I have spent it? 

He replied:  If the situation is as you describe, that is a reprehensible action which is not permitted. Rather it is a kind of betrayal. You have to return the money that you have taken in this manner to the state treasury. If you cannot do that, then you have to give it in charity to the poor Muslims or to charitable projects, as well as repenting to Allaah, and you must resolve sincerely not to do that again, because it is not permissible for a Muslim to take something from the Bayt al-Maal (treasury) of the Muslims except in ways that are permitted in sharee’ah, and that are known to and approved of by the state. 

Fataawa Islamiyyah, 4/312.