  This is a continuation of math.AG/0609741. Let Y be an affine symplectic
variety with a C^*-action with positive weights, and let \pi: X -> Y be its
crepant resolution. Then \pi induces a natural map PDef(X) -> PDef(Y) of
Kuranishi spaces for the Poisson deformations of X and Y. In the Part I, we
proved that PDef(X) and PDef(Y) are both non-singular, and this map is a finite
surjective map. In this paper (Part II), we prove that it is a Galois covering.
Markman already obtained a similar result in the compact case, which was a
motivation of this paper. As an application, we shall construct explicitly the
universal Poisson deformation of the normalization \tilde{O} of a nilpotent
orbit closure \bar{O} in a complex simple Lie algebra when \tilde{O} has a
crepant resolution.
