To always start Mozilla Firefox browser in private or anonymous mode directly, here’s how you can create a desktop shortcut icon;
Click Start and Right-click “Firefox”. Select More –> “Open file location”;
In the Windows Explorer window, right-click “Firefox” shortcut and click “Copy”;
On the Desktop window, press Ctrl+V or right-click any empty space to select “Paste” to copy the shortcut icon of Firefox browser on Windows 10 Desktop. Next, right-click the Firefox shortcut icon and select “Properties” in the menu;
Right next to the “Target” under the “shortcut” tab, you’d see a path of the Firefox.exe. Right after the inverted comma (“), enter;
(space) -private -window
or
(space) (hyphen)private (hyphen)window
and select “Ok” when done;
Next time, whenever you click on this desktop shortcut for Firefox, it will always open a new Firefox window in the private or anonymous browsing mode.
Courtesy:
https://developer.mozilla.org/en-US/docs/Mozilla/Command_Line_Options#-private
