I used a spudger around the edges of the outer case to gently ease it upward since I could not lift it out with my fingers. Then it came right out.
I would mark the top of the large inverter cable connectors somehow, with a marker or pencil. My connectors had writing on the bottom, not the top as pictured, and I bent the pins trying to reinsert it incorrectly since the top and bottom look similar. Nearly all the other connectors have an obvious top and bottom.