Covering graph conjecture for 2-token graphs of stars

Let $K_{1,n}$ be the star graph with $n$ leaves. Suppose that $n$ divides $\binom{n+1}{2}$. A combined voltage assignment $(\alpha,\omega)$ on a base graph $X$ with values in the group $\mathbb{Z}_{n}$ defines a covering graph $X^{(\alpha,\omega)}$.

Covering conjecture for 2-token star graphs. The token graph $F_2(K_{1,n})$ is isomorphic to a covering graph $X^{(\alpha,\omega)}$ of a base graph $X$ on $n-k$ vertices, with combined assignment on the group $\mathbb{Z}_{n}$.

The conjecture summarizes the preceding examples and discussion for 2-token graphs of stars; no resolution is supplied in the source.