When does the first cohomology group commute with inverse limit?

Question

Let $M_i,i\in\mathbb{N}$ be an inverse system of continous, discrete G-modules and let $M=\varprojlim M_i$. Under what conditions on $M$ and $M_i$ do we have $\varprojlim H^1(G, M_i) \cong H^1(G, M)$? I came across a paper that gives a criterion for commutativity with direct limits, but not inverse limits. Thank you!!