Edit*** It looks like I've actually configured this correct. HOWEVER, I think my issue has changed:

What I actually need this to do is inherit the department ID used in the timesheet (Completed in My Current Timesheets) so it is visible by people under 'timesheet activities'.

How do I achieve this? 

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OLD ISSUE:

I've been able to include the department that an employee belongs to when they fill out their timesheets. 

This is populated in the view by:

<field name='department_id'>

However, using the same department_id field in the 'Timesheet Activities' view results in an error: 

Field(s) `arch` failed against a constraint: Invalid view definition

Error details:
Field `department_id` does not exist