Star Of David Blue And White that Preceded the Israeli Flag

It is a well-known fact that the existence of the Magen David on the yellow patch in the period of the Holocaust was among the central reasons for its acceptance to the center of the Israeli flag. What is not so known, and to me at least was really shocking, is that the yellow patch was not uniform in all the places under the Third Reich regime and at least at the start there were a few blue Stars of David on a white arm band. It was somewhat like precursor of the Israeli flag. I wonder how such an important piece of information escaped the books that describe the development of the Israeli flag. IMHO we should make sure that future generations would know about it.
I found about this special badge on yadvashem site, where it says in Hebrew that on the first of December 1939 Hans Frank, Nazi governor in Poland, ordered the Jews to carry on their right sleeve and on their upper garment a white band and on it a blue Star of David. ten centimeters wide…In Lublin and in Zaglembie. From the 10th of July 1941 Jews in Bialistok had to wear on their right arm a white band and on it a blue Star of David…