What is the ruling on renting out personal equipment to an institution where one works, through an intermediary institution, such that the lessor has a preferential right to rent due to their position, and what is the ruling on the money resulting from this transaction?

It is not permissible for an employee to lease his equipment to his institution if he has a role in accepting or continuing this lease, because he is entrusted and must strive to achieve the institution's interest. This contradicts his pursuit of his personal interest. For this reason, it is not permissible for an agent to buy or sell for himself except with the permission of the principal. If the institution permits it, then there is no harm.