If I understood you correctly you want to save the .muse file version before syncing the changes made by your customer using In Browser Editing.
Whenever you client make changes to your live site using In Browser Editing you will get a prompt notifying the changes made in live site in Muse when you open that file.
1. At that point of time Click on cancel
2. Now Save the file as back up using File > Save site as
3. Reopen the original file and now review or merge the changes. In case you do not receive the prompt for review then you can force it from File > Sync with Web version
It is also advised to save the .muse file after every publishing done by you and keep its back up.
Note: If customer has made changes 10 times since you have open the file in Muse then you will only be able to get all the 10 changes in sync so you can have only one back up in this case.
Thanks for the answer.
Actually that is not what i meant.
I want my client to have an option after the website is live on his domain, to edit the content with In Browser Editing but not to publish the edited site but just to save changes and publish them when he want to share it with the world. You can look at it like a Draft Save...