On locally soluble $AFN$-groups

Let $A$ be an $\mathbf{R}G$-module, where $\bf R$ is a commutative ring, $G$ is a locally soluble group, $C_{G}(A)=1$, and each proper subgroup $H$ of $G$ for which $A/C_{A}(H)$ is not a noetherian $\bf R$-module, is finitely generated. We describe the structure of a locally soluble group $G$ with these conditions and the structure of $G$ under consideration if $G$ is a finitely generated soluble group and the quotient module $A/C_{A}(G)$ is not a noetherian $\bf R$-module.