@HaniefB4A script component actually requires a separate file (the CS file) to be included as well. The process of Adding an existing project item does not include these extra files and they would need to be handled manually. You can manually copy over the CS file and then copy the "Compile" node containing reference to it from the osproj file to actually make a copy of the script. You can open the osproj file in any text editor (like Notepad++ for example) and search for your cs file by name. You'll see a section where it is being included. This needs to be copied if you want to have your global container or automation have access to the script to compile it. This is not really my recommended approach however.

My suggestion would be to add any of your common scripts to a separate project. You can then reference this project from wherever you need access to it. That makes it such that you don't ever need to copy it and maintain multiple copies. You also would not need to alter the osproj file or edit any of the os files (which might potentially corrupt them).

As always though, before you make any changes, always create a backup of your solution directory and any projects it references before you make any changes like this.