2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/148287This 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.31 pages. To appear in Selecta Mathematica. A reference is updatedHigh Energy Physics - TheoryQuantum Algebratext