If $E$ is a finitely presented left $A$-module, then tensor product by E commutes with direct product.

Question

Please can anyone help me to prove this statement:

If $E$ is a finitely presented left $A$-module, then for every family $(F_i)$ of right $A$-modules the canonical homomorphism $\phi: E\bigotimes_A \prod F_i \rightarrow \prod (E\bigotimes _A F_i)$ is an isomorphism.

I have proved that the map is surjective, and I want anyone to help me to prove that the map is injective.

Thank you!