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Disable Private Browsing 18.104.22.168-signed.1-signed Requires Restart
Disable Private Browsing menu option and keyboard shortcut. If you also want to disable the deletion of history, use Disable Private Browsing Plus from https://addons.mozilla.org/en-us/firefox/addon/disable-private-browsing-pl/
About this Add-on
Since version 1.4 clearing the browsing history is also disabled. A side effect is that bookmarks can no longer be removed unless in Safe Mode. (You can still move them to a folder that you can name "Remove".)