Let $G$ be a profinite group, $A$ a free $\mathbb{Z}_p$-module of finite rank with a continuous action of $G$ and $B$ any $\mathbb{Z}_p$-module (I am not supposing it to be free), with the trivial action of $G$.

I am looking at continuous cohomology groups. I tought that $H^i(G,A \otimes B)$ would be isomorphic to $H^i(G,A) \otimes B$, which is false in general.

Is there a condition on $B$ making this statement true ?