Forum:Zanji V. Apprentice Magician

I have a question about Zanji's effect versus Apprentice Magician.

So player A controls 3 six samurai and that includes Zanji.

Player A uses Zanji to attack player B's Face Down Apprentice Magician.

Can player B use Apprentice Magician's effect because Zanji's effect activates at the "End of the Damage step"?