Unchanged simple-module restriction formulas at the special parameter $\theta=\delta/\gamma$

Let $\mathsf{qw}\kern-1.8pt\mathscr{B}_{m,n}$ be the quantum walled Brauer algebra with $\theta=\frac{\delta}{\gamma}$, let $\mathscr{C}\mathrm{r}_{m,n}$ denote the set of cross bipartitions in the $M=2$, $N=1$ case, and let $D(\lambda)$ be the corresponding simple module. Restriction-formula conjecture. For $\lambda\in\mathscr{C}\mathrm{r}_{m,n}$, the restrictions $\operatorname{res}^{m,n}_{m,n-1}D(\lambda)$ for simple modules over $\mathsf{qw}\kern-1.8pt\mathscr{B}_{m,n}$ are explicitly given by the formulas from the stated restriction theorem without any changes. The claim predicts that the formulas established for the corresponding endomorphism algebra remain valid for these quantum walled Brauer simple modules; the supplied text gives no resolution.