Is the manager sinful if he approves the leave of an employee who shirks work with excuses he knows are untrue?

It is not permissible for the head (of an organization/department) to approve requests for leave that he believes are invalid or most likely so, as this is a betrayal of trust and a lack of sincerity. He must investigate granting leave only for urgent needs that do not harm the work. Islam encourages fulfilling trusts and not betraying them.