Is what the employee did—submitting a lease contract with a value higher than the actual value to maintain the housing allowance which he believes is his right—considered Haram (forbidden), and is the money earned from it Haram?

If labor law grants the employee a housing allowance only up to an estimated maximum value, and the employee is entitled only to the actual rent, then the employer has the right to request a copy of the lease agreement. It is not permissible for the employee to submit a copy with a value higher than the actual rent. If the law states otherwise, the worker should demand their right through the competent authorities, and it is not permissible for them to lie or commit forgery.