When sharing tasks between lists, statuses will not align, and you are then unable to filter on the "shared-to" list. Filters should be expand and source filterable statuses from all items present on a list.

We are using the platform for large Project Management along with department-level task and effort management. For large projects, we will build a task schedule, and then add the relevant portions of said schedules to the departments that own those portions of the Project. When doing so, the original statuses are maintained, but in the department's list, they can only filter by their statuses.