If a dog owner cut its long fur very short would the dogs puppies have very short furtoo?

No, the length of a dog's fur is determined by its genetics, not by the length of the fur when it is cut. Puppies inherit their coat characteristics from their parents' genes, which dictate fur length, texture, and type. So, even if a dog owner cuts the mother's fur very short, the puppies can still be born with long fur if that is what their genetic makeup dictates.