Bleak et al. showed that the automorphism group of the Higman-Thompson group $V_n$ is given by conjugation by bi-synchronizing automata. Relaxing the bi-synchronizing condition produces injections from $V_n$ into itself, images of which are subgroups of $V_n$ that are isomorphic to $V_n$. In this talk, I will characterize such subgroups of $V_n$ as subgroups that preserve colorings of the infinite rooted $n$-art tree. This is joint work with Feyishayo Olukoya.