Here are some photos with the clothes out of the way so you can see the added wood to support the Closet Maid shelf/hanger. The wood sections are screwed into the side wall framing at each end of the closet. Most of the wall is hollow, so it is necessary to locate the framing inside the wall to secure the wood.
I could not get a screw into the internal wall framing on the back side of the cabinet at one end of the closet, so I used small "L" brackets to secure the added wood to the exposed framing. It's not elegant, but it works.
Closet Maid wall clips secure the back of the shelf to the rear wall of the closet. There is no tension on the shelf holding the added wood pieces. The wood is screwed to wall framing, and a Closet Maid end support holds up the shelf ends. It is really just a slight variation of a regular residential closet installation.