Rigged modules II: multipliers and duality

In a previous paper with Kashyap we generalized the theory of $W^*$-modules to the setting of modules over nonselfadjoint dual operator algebras, obtaining the class of weak*-rigged modules. The present paper and its contemporaneous predecessor comprise the sequel which we promised at that time would be forthcoming. We give many new results about rigged and weak*-rigged modules and their tensor products, such as an Eilenberg-Watts type theorem.