sliding glass door part inquiry

Thank you for reaching out to us! Before we recommend anything, can you show us a photo of the mortise lock? We would also like to see a photo of the mortise lock slot that takes the thumb lever. That should help with our search. 

Your handle set looks similar to the 82-032 and the 82-033 which have an internal plastic piece that lets you position the thumb turn in different locations. However, I am not sure either of these handles could work for your 1" thick door. For starters, you would need to purchase shorter screws to be used on your thinner door. The next issue would be with the key and thumb turn tail. Your thumb turn allows the key cylinder tail to go inside of the thumb turn. Whereas the 82-032 and 82-033's thumb turn and the key cylinder tail meet up inside the mortise lock. Take a look at the related videos on this page, especially the one on installing the key lock, and let us know if that helps. 

Another idea I just had would be to reuse your existing thumb turn to see if it will work with the newer handle set.