Marin–Wagner's kernel-generation conjecture for the Links–Gould representation

Let $b1\in\mathbb{C}\setminus\mathbb{Q}$, let $H_n(\alpha)$ be the cubic Hecke algebra through which the braid-group representation factors, and let $r_2$ and $r_3$ be the relations introduced by Marin and Wagner. Let $A_n(\alpha)=H_n(\alpha)/(r_2,r_3)$. Marin–Wagner's kernel-generation conjecture. For every $n\in\mathbb{N}$, the relations $r_2$ and $r_3$ are sufficient to describe the kernel of $\rho_n(\alpha)$; equivalently, there is an algebra isomorphism

$$A_n(\alpha)\simeq LG_n(\alpha).$$

The relations are known to give the required quotient for four strands, but the source presents their sufficiency for all numbers of strands as a conjecture.