Simple question on proving naturality of an adjunction

Question

Say you want to prove that there exists an adjunction between the functors $F:\mathcal{C}\to\mathcal{D}$, $G:\mathcal{D}\to\mathcal{C}$ with $F$ left adjoint to $G$, and suppose that the bijection on hom-sets $$\hom_{\mathcal{D}}(FA,B)\cong\hom_{\mathcal{C}}(A,GB)$$ has been established. Is it enough to prove naturality of $A$ and $B$ using the map $$\hom_{\mathcal{D}}(FA,B)\to\hom_{\mathcal{C}}(A,GB)$$ (or the opposite) or does one need to check both directions?