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.