Kahn's integral comparison conjecture for Weil motivic cohomology

Fix a smooth projective variety $X$ over $\mathbb{F}_q$ and an integer $n$. For every prime $l$, let $c$ be the comparison map from Weil-étale motivic cohomology to continuous $l$-adic cohomology. Thus the relevant groups are $H^i_W(X,\mathbb{Z}(n))$ and $H^i_{cont}(X,\mathbb{Z}_l(n))$.

Kahn's conjecture. For every prime $l$ and any $i$, the map $c$ induces an isomorphism

$$H^i_W(X,\mathbb{Z}(n))\otimes\mathbb{Z}_l\xrightarrow{\sim}H^i_{cont}(X,\mathbb{Z}_l(n)).$$

This would make Weil motivic cohomology an integral model for both $l$-adic and $p$-adic cohomology. The source identifies it with Kahn's conjecture, but the supplied text does not state whether it has been resolved.