  In this article, we study the behavior of the stability of pullback of a
vector bundle under a finite morphism from a (not necessarily smooth) stacky
curve to an orbifold curve. We establish a categorical equivalence between
proper formal orbifold curves and proper orbifold curves in the sense of
Deligne-Mumford stacks. Using this identification, we define the notion of
slope $P$-(semi)stability of vector bundles on proper formal orbifold curves
$(X,P)$. We establish some equivalent conditions for a stacky genuinely
ramified morphism, analogous to the case of curves. Finally, we show that for a
cover of an orbifold curve arising as a cartesian pullback via a genuinely
ramified morphism of smooth projective connected curves, the orbifold slope
stability is preserved under the pullback.
