Let $G$ be a finite group and let $M$ be a $G$ module. Denote by $M^G$ the set of elements in M which are invariant under the $G$-action. Consider the trace map $Tr:M\rightarrow M$ defined by $$m\mapsto\sum_{g\in G} g(m).$$
A known result which I am looking reference for saying that if $G$ is cyclic group then $$H^2(G,M)\cong M^G/\text{Im}(Tr(M)).$$
I was told that it suppose to be in any cohomology book, but I didn't found such reference. I hope someone here might know where to find it.
Thanks in advance.