The conjecture on étale pro-homology and pro-homotopy satellites

Let $X^{et}$ be the étale site from Example, let $A$ be an abelian group, and let ${\Greekmath 0119}_n^{et}(X)$ and $H_n^{et}(X,A)$ denote étale pro-homotopy and étale pro-homology. The étale satellite conjecture. The left satellites of $H_0$ are naturally isomorphic to étale pro-homology:

$$H_n(X^{et},A_{\#})\simeq H_n^{et}(X,A).$$

Moreover, the non-abelian left satellites of $H_0$ are naturally isomorphic to étale pro-homotopy:

$$H_n(X^{et},(\mathbf{pt})_{\#})\simeq H_n(X^{et},{\Greekmath 0119}_0^{et})\simeq {\Greekmath 0119}_n^{et}(X).$$

The claim proposes an étale-homotopy-theoretic application of the cosheaf satellite construction; the source does not state whether it has been proved or disproved.