Let $\mathcal{I}$ be a small category and $\mathcal{A}$ an abelian category. If $\mathcal{A}$ is complete (that is, the product of any set of objects exists) and has enough injectives, how can I prove that the functor category $\mathcal{A}^{\mathcal{I}}$ has enough injectives?

I know that if $R$ is a right adjoint functor to an exact functor $L$ then $R$ preserves injective objects. This may be used to solve the problem; there is a functor $R:\mathcal{A}^{\mathcal{I}}\rightarrow\mathcal{A}$ satisfying the proposition above? If yes, how can I prove it?