On Linux, the installer I have built creates a shortcut in my desktop and points to the right file, but it still does not work. The script works fine from the command line.
It may be that your script requires a specific working directory. If you find this issue, you can try passing the working directory to the script, and cd into it before running. As exec argument when creating the shortcut put :
${installdir}/example
Then, inside script add the following line at the beginning, after
#!/bin/sh:
cd \$1
That will cd into the correct directory before executing the rest of the script.