Let $R$ be any ring. $f$ is an idempotent of $R$ such that $fR$ is a faithful right module.
I have seen that "Since $fR_R$ is projective, the functor $fR \otimes_R-$ sends injective $R$-modules to injective $fRf$-modules." (I know that when $R$ is an artin ring, $fR \otimes_R-=Hom_R(Rf,-)$, and it induces an equivalence between $addI$ and injective $fRf$-modules, where $I$ is the injective envelop of $Rf/rad(Rf)$), I don't know how to get this result, thank you for any help.