Just a bit more on these patches Paul. The F or Fahrer (driver) patch was worn by HJ, BDM, DJ and JM personnel who drove staff cars at the various levels. In my original post I incorrectly stated that this was a Motor-HJ patch so although some of those who wore the patch would have been Motor-HJ the patch wasn't exclusive to that part of the HJ. With that in mind the F patch shouldn't really be seen as being aligned with the standard Motor-HJ patch and the Gebietsinspecteur.
The F patch was on red cloth with the F in aluminium thread and could only be worn by personnel on active service as staff car drivers. Those who had been staff drivers but who had then returned to normal duty were not permitted to wear the patch.
So, it would have been a rare patch during the period and of course is even rarer now.