My great-grandfather was born in Lemberg, Galicia (now Lviv, Ukraine). However, I am unsure how to proceed to further back in the family tree. I have written to the archives in Lviv which hold the records, however I have never heard back. The family name: Mühlgay and my great-great-grandfather's hebrew name: Mordechai (likely not his legal name) are all that I have to go on. I know that Mordechai Mühlgay's father was R' Yoshke (likely Josef or Jozef) of Czyczkow, a local religious leader, however I have little else. What information is available about my ancestors?
Although I am not giving the name of my great-grandfather, I will say that he and his brothers were born over the span of the late 1880s-1890s and that they moved to Fürth, in Bavaria, at some point of the latter decade.