Equivalence of domains arising from duality of orbits on flag manifolds II

S. Gindikin and the author defined a $G_{\mathbb{R}}$- $K_{\mathbb{C}}$ invariant subset $C(S)$ of $G_{\mathbb{C}}$ for each $K_{\mathbb{C}}$-orbit $S$ on every flag manifold $G_{\mathbb{C}}/P$ and conjectured that the connected component $C(S)_0$ of the identity would be equal to the Akhiezer-Gindikin domain $D$ if $S$ is of nonholomorphic type. This conjecture was proved for closed $S$ in the works of J. A. Wolf, R. Zierau, G. Fels, A. Huckleberry and the author. It was also proved for open $S$ by the author. In this paper, we prove the conjecture for all the other orbits when $G_{\mathbb{R}}$ is of non-Hermitian type.