>>17 I don't know how that works time-wise but it's still considered an adaptation of the anime: "The manga series written by Cain Kuga (久雅カイン?) based on the anime series Cowboy Bebop. It is an alternative telling of the story featured in the anime TV series."
It's not the same story anyway. And the original concept for Bebop belongs to the production team at Sunrise, not to any individual mangaka.