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A residually finite group $G$ has the Wilson-Zalesskii property if for allfinitely generated subgroups $H,K \leqslant G$, one has $\bar{H} \cap\bar{K}=\overline{H \cap K}$, where the closures are taken in the profinitecompletion $\widehat G$ of $G$. This property played an important role inseveral papers, and is usually combined with separability of double cosets. Inthe present note we show that the Wilson-Zalesskii property is actually enjoyedby every double coset separable group. We also construct an example of a LERFgroup that is not double coset separable and does not have the Wilson-Zalesskiiproperty.

On double coset separability and the Wilson-Zalesskii property