Let $R$ be a commutative ring, and let $M$, $M'$ and $N$ be $R$-modules. It is known that $Ext^1(M,N)$ is the set of isomorphism classes of extensions of $M$ by $N$, and is an abelian group under the Baer sum.
Consider the morphism of abelian groups $[f]\colon Ext^1(M,N)\rightarrow Ext^1(M',N)$ which maps an extension $[E] \in Ext^1(M,N)$ to its pullback by $f\colon M'\rightarrow M$ in $Ext^1(M',N)$.
Question: What additional assumptions do we need to ensure that $[f]$ is injective? Is it there a book where this problem in particular is addressed?