Can the renter rent out the house that he is renting?

Firstly: 

It is permissible for the one who is renting a house or anything else to rent it out or rent out part of it to someone else, for the same rent that he is paying or for more or less, because by renting the house he has become the owner of its usufruct, and he may dispose of that usufruct by giving it, renting it out or in other ways, so long as the second renter is going to use it in the same manner as him or less; if he has rented it to live in it, he does not have the right to rent it out to someone who will use it as a workshop and the like. 

This is the view of the majority of fuqaha’. 

Ibn Qudaamah (may Allaah have mercy on him) said: It is permissible for the renter to rent out the rented property if he has taken control of it. This was stated by Ahmad and it is the view of al-Shaafa’i and ashaab al-ra’y. 

It is not permissible to rent it out except to someone who will use it in a similar way, or in a manner that will cause less wear and tear.  

And it is permissible for the renter to rent out the property, for a similar rent or for more. This was stated by Ahmad and it is the view of al-Shaafa’i. End quote. Al-Mughni (8/54-56). 

The scholars of the Standing Committee for Issuing Fatwas said: If a person rents a house, apartment or showroom, for example, for a period of time, and he has some time left, it is permissible for him to rent it out to someone like him for the remainder of that period, for less or more, without any unfairness. 

Shaykh ‘Abd al-‘Azeez ibn Baaz, Shaykh ‘Abd al-‘Azeez Aal al-Shaykh, Shaykh ‘Abd-Allaah ibn Ghadyaan, Shaykh Saalih al-Fawzaan, Shaykh Bakr Abu Zayd. 

Fataawa al-Lajnah al-Daa’imah (15/92). 

Shaykh Saalih Fawzaan al-Fawzaan (may Allaah preserve him) said: If a person rents a place for a certain amount of time, he has the right to live in it for that period, or to rent it out to someone else who will use it for a similar purpose, or one that causes less wear and tear, i.e., he may make use of the place himself, or allow someone else to do so. End quote. 

Al-Muntaqa min Fataawa al-Fawzaan (3/221, question no. 336). 

But, if the owner has stipulated that you should not rent it out, then you must abide by this condition, because Allaah says (interpretation of the meaning): “O you who believe! Fulfil (your) obligations” [al-Maa’idah 5:1]. 

And Allaah knows best.