Is it permissible for the tenant to lease the rented property to a third party without the owner's knowledge, and is it permissible for the owner to stipulate to the tenant that subleasing is not allowed?

It is permissible for the tenant to sublease the rented property to a third party during the contract period, as long as the property is not adversely affected by a different user. The owner's knowledge of this is not a prerequisite.

However, if the contract includes a condition prohibiting subleasing to a third party, then Muslims are bound by their conditions. It is permissible for the owner to stipulate that the tenant may not sublease the rented property to a third party.