  This is the second part in a series of papers presenting a theory of tensor
products for module categories for a vertex operator algebra. In Part I
(hep-th/9309076), the notions of $P(z)$- and $Q(z)$-tensor product of two
modules for a vertex operator algebra were introduced and under a certain
hypothesis, two constructions of a $Q(z)$-tensor product were given, using
certain results stated without proof. In Part II, the proofs of those results
are supplied.
