Is it permissible for an engineer to take a portion of a contractor's work at a lower price than the company's value, and then assign it to other craftsmen at an even lower price, keeping the difference, knowing that neither the company nor the employer is aware of or permits this?

It is not permissible for an employee to engage in transactions unauthorized by the company, as Allah the Almighty says: (O you who have believed, fulfill [all] contracts), and the Prophet, peace and blessings be upon him, said: "Muslims are bound by their conditions." This condition is binding whether written or known by custom. Similarly, it is not permissible for a contractor to delegate another to perform a task which the employer stipulated he must perform himself.