In Web TimeSheet it is possible to allow a Approver/Manager/Supervisor to book timeoff for another user or employee, to do this follow these steps:

1] Log into Web TimeSheet with administrative rights. 
 
2] Click on 'Administration' icon at the top. 
 
3] On the left side pane, under 'Users/Departments' click on 'Permissions'
 
4] Click on the edit button on the required permission that you need to edit.
 
5] Under 'System' expand 'Administration' ensure 'Submit' is checked next to Historical Time Off.
Note:- Please refer the attached screenshots for illustrated steps.