Completeness conjecture for the relations of the Weyl-group algebra $\Lambda_w(B_n)$

Let $B_n$ be the Weyl group of type $B_n$. Let $\Lambda_w(B_n)$ be its left-invariant differential algebra, and let $\Lambda_{quar}(B_n)$ be the quotient of the quadratic algebra $\Lambda_{\quad}(B_n)$ by the quartic relations displayed in Example 2.1 and Remark 2.3. Completeness conjecture. The relations in those examples are the complete set of relations, equivalently

$$\Lambda_w(B_n)\cong\Lambda_{quar}(B_n).$$

This conjecture concerns whether the quadratic and quartic relations completely present the differential algebra for type $B_n$. The source gives no evidence of resolution.