  We determine, under a certain assumption, the Alexeev-Brion moduli scheme M_S
of affine spherical G-varieties with a prescribed weight monoid S. In [
arXiv:1008.0911 ] we showed that if G is a connected complex reductive group of
type A and S is the weight monoid of a spherical G-module, then M_S is an
affine space. Here we prove that this remains true without any restriction on
the type of G.
