The only way this works is if the 2 parents are both heterozygous for fur color. So each parent is Ff (I'm using F for fur color where F is black and f is white).
The two Ff parents would have had to come from two parents that had FF and ff as their genotypes (so a homozygous black mouse and a homozygous white mouse).
You can check these by Punnet Square starting with the p0 generation and cross FF and ff; you get all Ff.
Then do another Punnet Square crossing Ff with Ff and you get 50% progeny Ff (black) and 50% ff (white).