Lock fell down inside patio door frame

Hello there. I have a patio door that had the little lever break and it would not lock. Stupid me unloosened the screws and when I did, the lock fell inside of the frame. At this point, my #1 goal is to get a replacement lock in there. I don't even care if the old lock stays in the frame. It only makes a slight rattle but I need to lock this door. It appears the distance between holes on the plate is just a shade under 10 inches. The 9 7/8 mortise lock you sell looks like it would fit in place. My question is would I just use that lock and can I still use my handle and the other part it connects to? I am attaching pics of the 3 main parts. I can't send a pic of the lock because it fell obviously.
Thanks
Bill