Is it permissible to lease unused hospital equipment and utilize the rental income for the hospital's benefit without the owner's knowledge, given that the director is responsible for and manages the hospital's affairs?

If the manager's action falls within his scope of work according to the contract or common practice in his field, then there is no harm. Otherwise, the owner's permission is necessary, because the manager is an agent bound by the limits of the agency, and he must not exceed his principal's authorization. Ibn Qudamah said: "The agent does not have the authority to act except within what his principal's permission necessitates, whether explicitly stated or by common practice." In the Fiqh Encyclopedia, it states: "The agent executes the agency within the limits authorized by the principal, or those restricted by Islamic law or common practice."