Divisibility conjecture for Conway polynomials of links in rational homology spheres

Let $K$ be a null-homologous oriented $k$-component link with zero pairwise linking numbers in a rational homology sphere $\Sigma$, and let $L$ be an admissible link of $ell$ components in $(\Sigma,K)$. Divisibility conjecture. Then

$$z^{2k-2+\ell}\text{ divides }\nabla_K([\Sigma,L]).$$

This conjecture generalizes the preceding divisibility theorem from knots to links and is intended to study Conway polynomials of manifolds with higher first Betti number. The case $\ell=0$ was recently proved by Levine, while the general case is unresolved in the supplied source.