No, your Carl Hoff is different than mine. Mine had no Frank as a child but did have a Gustav. He was also married to an Ernestine Korth here in Texas. My Carl Hoff also passed away in Tucson, AZ, Jan 23, 1890. I don't know much about your line of Hoff's but I dod know it made my research more difficult in the beginning.
I wish you best of luck in your research.