Is it permissible for an employee to leave work early with the permission of his supervisor, and to sign that he completed the full working day on the following day, to avoid a deduction, knowing that his daily tasks have been accomplished?

An employee must adhere to the agreed-upon working hours, because Muslims are bound by their conditions. The employee is a private contractor who must abide by the full working hours, and it is not permissible for him to leave before their end except with the employer's permission or according to regulations. Seeking permission from an unauthorized supervisor does not make leaving permissible.