If a person is hired to do a job, it is permissible for him to hire someone else to do it

There is nothing wrong with selling jobs or contracts. This
is like when a person is hired to do some construction work or the like;
there is nothing wrong with him hiring someone else to do the actual work,
but that is subject to two conditions: 

-1- 

The institution should not have stipulated in its contract
that the person hired must do the work himself and must not sell it to a
third party, because the Prophet (peace and blessings of Allaah be upon
him) said: “The Muslims are bound by their conditions.” Narrated by Abu
Dawood, 359; classed as saheeh by al-Albaani in Saheeh Abi Dawood. 

The Standing Committee
was asked about someone who rented a building for 100,000 and sublet it for
150,000 – is that permissible? 

They replied: 

Whoever rents a building may sublet it to someone else for
the same price as that for which he rented it, or for more or less than
that, and for the same time period as that agreed upon or less, not for more
that may cause harm, because he has the right to make use of the thing that
he has rented. Therefore it is permissible for him to make use of it himself
or let someone else make use of it, unless the owner has stipulated that the
renter may not transfer it to someone else, or he may not rent it to those
who practice certain professions or occupations, in which case they are both
bound by the conditions that they have agreed upon. 

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

Question: If a person is hired to do a certain job, such as
if it is said, ‘We want you to clean this house every day, and we will give
you one hundred riyals each month,’ then he hires someone to clean the house
each month but for fifty riyals, is that permissible or not? 

Answer: Yes, that is permissible. This is like saying that it
is permissible to rent what’s left of a lease for more than what one has
paid in rent. This is what people do nowadays, for example we see that the
government has an agreement with a company to clean the mosques, so each
mosque is cleaned in return for a certain amount of money, then this company
gives the workers who do the work agreed upon in the contract less than
one-quarter of what the company has agreed upon with the government.
… 

For example: I hired a
man to copy Zaad al-Mustaqni’ (a book of fiqh) for me, and I knew
that this man’s handwriting was excellent and that he makes few mistakes,
then he hired a man to write it for less than I had hired him, and the
handwriting of the man who was hired by the one whom I had hired was
beautiful. But the scholars say that this is not permissible. 

Al-Sharh al-Mumti’, 4/327 

That is because what matters when it comes to copying books
is not that the handwriting should be beautiful, rather what matters is both
beautiful handwriting and attention to the rules of spelling and placement
of diacritical marks, etc. 

And Allaah knows best.