Any / All Tools can be moved... Rated 1 out of 5 stars
Any / All FF Tools can be moved to and removed from the bar without using an addon.
Simply Right Click in a blank area of the FF Menu Bar or Tool Bar and select Customize from the drop list. This will open the built in FF Customize Toolbar app. Any of the several tools can be dragged between the app & the toolbar. Tools may be placed almost anywhere on either the Menu or Navigation Toolbars.
My preference includes placing the Add New Tab Button tool between the FF Address Window and the Search Tool where it is conveniently accessed for a new search. In this location it is never clicked by accident. The Open New Window Button may be placed there as well.