Using regular expressions to get a folder three levels deep

I'm having trouble figuring out how to write a regular expression to achieve the following:

Source File Tree:

-Active Projects
----Project Name
------Internal Documents
--------Budget_Schedule\*
--------Design
--------Procurement
----Project Name2
------Internal Documents
--------Budget_Schedule\*
--------Design
--------Procurement
----Project Name3...

Desired Destination File Tree:

-Project Name
----Internal Documents
--------Budget_Schedule\*
-Project Name2
----Internal Documents
--------Budget_Schedule\*
-Project Name3...

I only want the Budget_Schedule folder and its contents and to maintain the parent folder structure. Is this possible?