Out of the box there is no such functionality that you describe. You can only log time for the user you are logged in with. However, it seems that the add-on Tempo Timesheets allows such a function. In their documentation there is a configuration option User with Approve Timesheet Permission can log work for team members.
This could be what you want. But this add-on is commercial. I'm not sure if you are willing to pay the price just for that functionality.
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