Fact A : If $E_i$ is a directed system of $R$-modules, and $F$ is another $R$-module. Then
$$\varinjlim(F\otimes E_{i})=F\otimes(\varinjlim E_{i}).$$
Fact B : "Every module is a direct limit of its finitely generated submodules."
How does Fact A implies Fact B?
Serge Lang claims this in his Algebra book.