Closure operators in modules and adjoint functors, II

In this work we study the relations between the closure operators of two module categories connected by two adjoint contravariant functors. The present article is a continuation of the paper [1] (Part I), where the same question is investigated in the case of two adjoint covariant functors.
An arbitrary bimodule $_RU_S$ defines a pair of adjoint contravariant functors $H_1=Hom_R(\text{-},U)\colon R\text{-}\mathrm{Mod}\to\mathrm{Mod}\text{-}S$ and $H_2=Hom_S(\text{-},U)\colon\mathrm{Mod}\text{-}S\to R\text{-}\mathrm{Mod}$ with two associated natural transformations and . In this situation we study the connections between the closure operators of the categories $R\text{-}\mathrm{Mod}$ and $\mathrm{Mod}\text{-}S$.