  This article is the second part of the article we promised to write at the
end of Section 1 of [FOOO15] (arXiv:1209.4410). (Part I appeared in [Part I]
(arXiv:1503.07631).) We discuss the foundation of the virtual fundamental chain
and cycle technique, especially its version that appeared in [FOn] and also in
Section A1, Section 7.5 [FOOO4], Section 12 [FOOO7], [Fu2]. This article is
independent of our earlier writing [FOOO15]. We also do not assume that the
readers have any knowledge on the pseudo-holomorphic curve. In this second
part, we consider a system of spaces with Kuranishi structures (abbreviated as
a K-system) and its simultaneous perturbations.
