Extension of scalars functor essentially surjective.

Question

Let $f:A\rightarrow B$ be a morphism of rings. When is every $B$-module $N$ of the form $M\otimes_A B$ for some $A$-module $M$?. What are sufficient and necessary conditions on $f$? I know for instance that if $f$ is $A\rightarrow S^{-1}A$ then this is true (take $M$ to be $N$ regarded as an $A$-module).