If $Y \to X$ is a finite etale map of schemes, then there exists a finite Galois morphism $Z \to X$ (i.e. it's a $Aut(Z/X)$-torsor) that factors as $Z \to Y \to X.$ The case when $X$ is normal is easy to prove: take the galois closure of function field of $Y$ and then take the normalization of $X$ in it. The general case is proved in Murre's book.
My question is, is this true for stacks? Namely if $Y \to X$ is a representable finite etale map of algebraic stacks, can it be refined to a representable Galois morphism $Z \to X?$