How can users see a ticket MOVED to a different department without being a member of that department?

How can users see a ticket MOVED to a different department without being a member of that department?

Our Engineering department doesn't want the rest of the company to be able to assign tickets directly to anyone in their group.

In order to stop that, we created Engineering as its own department.   Now however when we move tickets from Support to Engineering, we lose visibility to track the progress and we have no way to keep the customers informed.

Is there a way for Support to search tickets assigned to a different department without being a member of that department?