Is the target location exactly the same when you right-click and view the properties of the desktop icon and taskbar icon? (You'll probably have to right-click again on the Firefox icon that appears in the jump list when right-clicking the taskbar icon to get to the properties)

The target of the Desktop icon is: "C:\Program Files\Mozilla Firefox\firefox.exe" The target for the firefox icon on the Taskbar is also: "C:\Program Files\Mozilla Firefox\firefox.exe". I checked again and the Desktop icon opens up Firefox and it operates seemingly correct but the previous tabs are not opened.