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On the “Log Work” dialog you have access to Filters section and the dialog will remember you selected filter, and it will default to that filter every time you have opened it.
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If there are organization level issues, for which users need to log work in every period, you can use “Issues Setting” to mark these issues as “Always displayed on the timesheet”. These set of issues will be automatically included in every user’s timesheet, and they will be able to log work for these issues by just double clicking on a cell.