Let $\pi:X\to\mathcal X$ be a presentation of an Artin stack $\mathcal X$ of finite type over a field $k,$ and let $f:Y\to X$ be a finite 'etale covering. Does there exist a finite 'etale covering $Y'\to X$ factoring through $Y,$ such that $Y'$ can be given descent structure, i.e. there exists an isomorphism $pr_1^*Y'\cong pr_2^*Y'$ over $X\times_{\mathcal X}X$ satisfying cocycle condition, so that $Y'\to X$ descend to a finite 'etale covering $\mathcal Y\to\mathcal X$?