Schimpf badge - 3 Fallschirmjäger division

[WARNACH]

I would like to show you my metal insignia of the 3 th Fallschirmjäger Division.


Top: July 1944 Original division-pin
Middle: (wooden !) veteran pin 1950's ???
bottom: 1969 veteran pin



Top: again the 1969 veteran Pin for comparison reason
bottom: stickpin - miniature 1960 - 1970's




The 2013 repro "small" pins "New" and "Aged"


Does anyone know the story of the wooden pin?
(IMO early postwar attempt to recreate the divisional pin for veteran meeting purpose - in 1952 the Fallschirmjäger founded their Bund deutscher Fallschirmjäger.)

Are there other forms that exist?

Thanks
Peter