How to attach a cat door to a screen

The problem was how does one attach a cat door to a screen?  We needed a solid locking door as he's not allowed out at night (too many cat, raccoon, etc fights) and to keep the squirrels out, they totally destroyed the cushions on our chairs. 

With an anchor point on one side only I didn't think it would hold up to daily use.  And it was too low for easy access, so quickly it was clear I needed a raised sill.  

First plan, replace the flap with high sill and medium cat door, however after consideration, he's a 20 pound cat, I went with the larger dog sized door and placed it to the left.

Then I used a lower sill 2x4 and framed the top and right sides with wood and attached with 3 hole angle brackets and a long deck screw on the right.  This made the door rock solid and gave me a good attachment for the screen.  Note the top and left framing boards extend beyond the edge of the door so I have some place to attach the screen. 

The white plate at the left slides in to lock the door.

I put some scrape wood around the outside to grip the screen in place securely.  Since it's a prototype build I just used whatever scrap wood I had.