Module Problem (about M-injective modules)

Question

Let $U, M$ be $R$-modules. Show that the following assertions are equivalent:

(a) $U$ is $M$-injective;

(b) every morphism $f : I → U$, $I$ a left ideal in $R$, with $R/ \ker f ∈ σ[M]$, can be extended to $R$.