Do you mean the save system for saving and loading your actual Twine project, or the save system within the respective story format for the end-user to save their progress while playing? I thought you were talking about the latter at first, but now I think you might be talking about the former. If you are, it seems like you just need to make use of the archive feature, which allows you to create a backup of all your story projects, and it can be created and imported into either the web version or the installable version.
You can also compile your project to html and import it back into Twine if you'd rather not use an archive. In this case, you just build your project as normal.
If you're talking about the latter, we need more to go on: what story format are you using and how do you want this feature to work, exactly? Note that the SugarCube 2 format supports importing and exporting saved data already. (SugarCube 1 does as well, but you should use 2.)