Get the name of shortcut

I have a scenario where I have 2 shortcuts for the same exe (3rd party exe). Say S1 and S2. When they are running I have 2 processes in task manager say app.exe and app.exe

I can get the PID, handle of the process but what I want to get is the name of the shortcut that is attached to the launch of the process. Is it possible to get the name of shortcut which launched the process somehow?

Note, this is a 3rd party app so I have no control over it. Had it been my app, I could have coded it to accept some argument etc etc and tracked it.

I sure doubt that it is possible.
 
What happens if you change the shortcuts to pass arguments? Does the application ignore the arguments? If so then you can differentiate betweeen the two shortcuts by using arguments.