Stable dual-surjunctivity for NUCA with uniformly bounded singularity

Let $G$ be a finitely generated group and let $A$ be a finite alphabet. Let $M\subset G$ be finite, let $S=A^{A^M}$, and let $s\in S^G$. Suppose that the NUCA map $\sigma_s\colon A^G\to A^G$ has uniformly bounded singularity and is stably post-surjective. Stable dual-surjunctivity. Then $\sigma_s$ is stably invertible. This is the dual surjunctivity analogue for non-uniform cellular automata with uniformly bounded singularity. The supplied text presents it as one of the conjectures motivated by the paper's results and gives no resolution.