notation note: the arrows indicate the path of the ball, so for instance Qe5->a1 means the Queen moves to e5 and plays the ball to a1.  If there were, say a rook on a1, the path would countinue, e.g. Qe5->a1->a8.

White plays

>!1.Qh1->f1->e1->d2. If black plays 1...Bxc3, white responds with 2.Kd2->c1->a2->a4 followed by 3.a4->b5, or, if 2...bxa2, 3.Ba4->b5. If black plays 1..Qxe5, white plays 2.Bd2->e1->f1->h1->a8.  If black plays anything other than 1...Bxc3 or 1...Qxe5, white plays 2. Bd2->b4->a5. White wins.