You can authorize another user to manage your Web TimeSheet tasks by assigning him/her as a substitute user. Web TimeSheet supports two types of users, Internal Users and External Users. Internal Users are Licensed Users. Substitute users are of type Internal Users. So, you can have an internal user substitute for another internal user, and an internal user can substitute for an external user.
External Users do not require a license in Web TimeSheet and are generally the users who are external to the organization. Hence, you cannot have an external user substitute for another external user or an internal user.