The token-reconstruction-family conjecture

Let $G$ be a graph, let $F_k(G)$ denote its $k$-token graph, and let a $k$-token reconstruction family of $F_k(G)$ be a family of subsets as defined in the source. Let $cmathcal{R}$ and $cmathcal{R}'$ be two such reconstruction families, and let $cmathrm{Aut}(F_k(G))$ denote the automorphism group of $F_k(G)$. Token-reconstruction-family conjecture. There exists $cpsicincmathrm{Aut}(F_k(G))$ such that

$$cmathcal{R}'=\{cpsi(X):X\incmathcal{R}_\varphi,\}$$

The source presents this as a reformulation of the preceding reconstruction conjecture using a proposition about $k$-token reconstructions. The supplied excerpt does not establish whether this reformulated conjecture has been resolved.