There are two settings that allow to fill in a timesheet on somebody's behalf. One of them is a custom setting that allows all supervisors to see and edit their teams' timesheets and the other one is a security item which allows specific profiles or users (depending on your Security Mode in custom settings) to see and edit everyone's timesheet.
Only System Administrators have access to those settings.
How to allow supervisors to fill in timesheets on somebody's behalf?
1) Open Setup.
2) Go to Custom Settings. You can type Custom Settings into the Quick Find/Search field or extend the Develop option and select Custom Settings.
3) Click the Manage button next to Preempt Global Settings.
4) Then click Global.
5) Click Edit and tick the Manager Can Fill Timesheets checkbox. Then click Save.
6) Now when you go to MyPrecursive page, you are able to select your team members from the resource name drop down in the Timesheets tab. You can fill in the timesheet and submit it.
7) To have the possibility to also recall your team members' timesheets even in approved status, you need to have the security item can_fully_recall_timesheets set to 'Y' on your profile or user (it depends on the 'Security Mode' setting in Preempt Global Settings, if it is set to 'Security Items' - you can set security items only on profile level, if it is set to 'Precursive Profile' - you can set security items on user level).
How to allow specific profiles or users to fill in timesheets on somebody's behalf?
1) The security item can_see_resources_as_admin gives the permission to see and fill in timesheet on somebody's behalf. To additionally have the possibility to fully recall those timesheet you need to have the security item can_recall_timesheet and can_fully_recall_timesheet to 'Y on yor profile. Thanks to that, you can give this permission to users which are not assigned as supervisors but should be able to fill in timesheets on somebody's behalves. Set both security items on the profile or user, depending on your Security Mode setting in Preempt Global Settings.
Click on the link to find the information on configuring security items: How to configure security items?