Is it permissible for a main contractor to take a sum of money as a gift from a subcontractor after the work has been completed and the amount deposited into his account without his prior knowledge, and is this considered a bribe or a gift?

This is a clear bribe, and it is impermissible to give or accept it, for the are Prophet, peace and blessings be upon him, cursed the one who gives a bribe and the one who takes it. Moreover, it falls under the category of gifts to employees, which is considered embezzlement. Therefore, the engineer should not take it except with the permission of his employer, and it appears to be a bribe intended to influence him.