SQLite does not support the FULL OUTER JOIN query.
To realize the desired query result adequate to a FULL OUTER JOIN query you can perform two LEFT JOIN queries, and combine the result with a UNION ALL command in the follow way:
SELECT employee.*, department.* FROM employee LEFT JOIN department ON employee.DepartmentID = department.DepartmentID UNION ALL SELECT employee.*, department.* FROM department LEFT JOIN employee ON employee.DepartmentID = department.DepartmentID WHERE employee.DepartmentID IS NULL
Above example performs a FULL OUTER JOIN of employee and department tables.