Suslin's conjecture for Lawson homology with coefficients

Let $A$ be an abelian group and let $X$ be a smooth quasi-projective variety of dimension $n$. Let

$$\Phi_{p,k}:L_pH_k(X,A)\to H_k(X,A)$$

be the natural transform from Lawson homology to singular homology. Suslin's conjecture for Lawson homology with coefficients. The map $\Phi_{p,k}$ is an isomorphism for $k\geq n+p$ and is an injection for $k=n+p-1$. The source describes this conjecture as essential to the structure of Lawson homology for smooth quasi-projective varieties, but gives no resolution in the supplied text.