When Is the Group $\operatorname{Hom}(A,B)$ an Injective $E(B)$-Module?

Injectivity conditions for the homomorfism group $\operatorname{Hom}(A,B)$ regarded as a left module over the endomorfism ring of the group $B$ are found for arbitrary Abelian groups $A$ and $B$, where $B$ is nonreduced.