Przytycki's Homflypt skein module conjecture for submanifolds of rational homology spheres

Let $M$ be a submanifold of a rational homology sphere. Assume that $M$ contains no closed, oriented incompressible surface. Let ${\cal S}_3(M)$ denote its Homflypt skein module, let $R\hat\pi^o$ be the module spanned by conjugacy classes of nontrivial elements of the fundamental group of $M$, and let ${\bf S}$ denote the symmetric tensor algebra. Przytycki's Homflypt skein module conjecture. The module ${\cal S}_3(M)$ is free and isomorphic to the symmetric tensor algebra over $R\hat\pi^o$:

$${cal S}_3(M)={\bf S}R\hat\pi^o.$$

This conjecture proposes that, in the absence of closed oriented incompressible surfaces, the Homflypt skein module is completely determined by conjugacy classes of nontrivial elements of the fundamental group. The supplied text does not indicate whether the conjecture has been resolved.