Generalized coinvariant-algebra isomorphism for finite Coxeter groups

Let $(W,S)$ be a finite Coxeter system, let $BE(W,S)$ be the associated algebra, and let ${\bf R}[\theta_s\mid s\in S]$ denote the subalgebra generated by its Dunkl elements. The coinvariant algebra of $W$ is denoted by ${\bf S}_W$. Generalized coinvariant-algebra conjecture. The subalgebra generated by the Dunkl elements is canonically isomorphic to the coinvariant algebra:

$${\bf R}[\theta_s\mid s\in S]\simeq {\bf S}_W.$$

The paper proves this for Coxeter groups of classical type and for $I_2(m)$, and conjectures the same statement for every finite Coxeter group.