Thank you Josemann57,
To know the correct translation is very useful. The variation between the 1951 Libyan flag and the representation seen in this badge is quite pronounces. The badge is professionally made and looks to be a Bevo construction. It was suggested that this badge was the fore runner to to flag adopted in 1951, designed by Omar Faiek Shennib, and even that it was the inspiration of the later flag, however, that is conjecture & speculation.
I suspect Ulsterman was very close to the mark with his suggetion it is a locally worn jacket for locals, possibly under control of the Axis powers.
Still hunting for images.