At this point, we'll want to cover the French Cleat, as you won't want it to be seen after installation.
Cut a 1x2 to 46-1/2" in length. Using the finish-head nails, attach this piece to the top of the case's back. Place the 1x2 perpendicular to the back, and drive the nails through the top of the back as well as the shelf standards into the 1x2. (This 1x2 will serve as a nailer for the piece of plywood to cover the French Cleat.)
Next, reach inside the assembly and measure from the top of inside of the box (just in front of the wedge) down to the bottom of the nailer you just installed. The distance should be six inches, but it's best to verify before cutting the plywood.
Once you have verified this distance, cut a piece of 1/4" plywood to 46-1/2" by this approximate 6" width. Then, nail the piece into both the wedge and the nailer. This should completely cover the wedge bracket and provide a much more aesthetically pleasing look to the back of the assembly.