He was sent overseas to study and they gave him a complete salary by mistake

If the system dictates that you should have half of the
salary whilst you are overseas, it is not permissible to you to take
anything more than that. What you have to do is tell those who are in
charge, regardless of whether the person who made the mistake will be
published or not. 

Shaykh Ibn Baaz (may Allah have mercy on him) was asked: I am
an employee working in a government department and sometimes they pay us
overtime without us having worked overtime and without us having attended
for work, and they regard that as a bonus for employees from time to time.
Please note that the head of the department is aware of that and approves of
it. Please advise us, may Allah reward you with good: is it permissible to
take this money? If it is not permissible, what should I do about money that
I have taken in the past, which I have disposed of? May Allah reward you
with good. 

He replied: If the situation is as you have described, that
is wrong and is not permissible; rather it is a betrayal. You have to give
back whatever you have taken in this manner to the state funds. If that is
not possible, that you have to give it in charity to poor Muslims or to
charitable projects; you also have to repent to Allah, may He be glorified,
and resolve sincerely not to do that again, because it is not permissible
for a Muslim to take anything from the bayt al-maal (treasury) of the
Muslims except in legitimate ways that the state knows of and approves of.
And Allah is the source of strength. 

End quote from Fataawa al-Shaykh Ibn Baaz, 19/344 

And Allah knows best.