Im very interested in this post because I also have a badge just like this also marked Brehmer Berlin however I can state with almost complete certainty its genuine.
It belonged to a paratrooper called Werner Ratzmann,I also have his Ground Assault badge his kit issue book,a photo of him in uniform and his iron cross.I also have documentation of his incarceration in a POW camp in Belgium,and his eventual move to another POW camp in England.
And I actually knew the guy although I was very young at the time !