Let $\text{Sm}/k$ be the category of smooth schemes over a field $k$ with etale topology. Suppose $\text{Sh}_{et}(\text{Sm}/k,\Lambda)$ be the etale sheaves of $\Lambda$ modules and the derived category of complexes of etale sheaves will be denoted by $D^b(\text{Sh}_{et}(\text{Sm}/k,\Lambda))$. I seem to have seen that \begin{equation} \text{Hom}_{D^b(\text{Sh}_{et}(\text{Sm}/k,\Lambda))}(\Lambda(X),\mathcal{F}^*[n])=\mathbb{H}^n(X,\mathcal{F}^*) \end{equation} where $\Lambda(X)$ is the etale sheaf represented by $X$ which is considered as a complex concentrated at degree 0. Could any one give a proof?
I guess this is also true in general.