I'm trying to remove a Falcon door lock that was installed around 2007. I hope to replace it with a Nest x Yale lock. I don't know the exact model of the current lock. It doesn't look like Falcon makes this type of lock anymore, though this is the closest current model I could find: Falcon MA series. I was able to remove half the lock. It seems that something inside is preventing me pulling the final piece out. See attached photos.
There's a retaining screw that holds the key cylinder in place -- you've already removed it.
Now put the key in the cylinder halfway (wrong key works better btw) and use it to unscrew the lock cylinder and remove it. You should be able to pop the front face plate off.
Remove the handle and spindle, and then you should be able to pull the mortise lock out from the side.
Lock cylinders are threaded and screw into the mortise lock body sandwiched in the door frame. The screws on the mortise body that go into the door frame simply keep it from rattling around too much and keep everything aligned.
The lock cylinder retaining screws slide into the cutouts in the lock cylinder and keep you from unscrewing it.
You may also have to remove the retaining screw on the outer door handle, but usually you can remove the outer door handle by pushing the shaft connecting the inner and outer door handles through the door. Make sure that you keep the door from shutting after this, as you'll have a hard time opening it otherwise.