The left exact functor $Hom_A(X,-)$

Question

Let $A$ be an finite dimensional algebra over a field K. Given a short exact sequence $0 \rightarrow L \rightarrow M \rightarrow N \rightarrow 0$ of $A$-modules, we know the functor $Hom_A(X,-)$ is a left exact functor, where $X$ is a $A$-module. So the sequence $0 \rightarrow Hom_A(X,L) \rightarrow Hom_A(X,M) \rightarrow Hom_A(X,N)$ is still exact. Now Suppose there is a infinite exact sequence of $A$-modules $0 \rightarrow M_0 \rightarrow M_1 \rightarrow M_2 \rightarrow \dots$, I think the sequence $0 \rightarrow Hom_A(X,M_0) \rightarrow Hom_A(X,M_1) \rightarrow Hom_A(X,M_2) \rightarrow \dots$ is also exact. Is that right?