Consider a representation of a finite group $G$ as automorphisms of a power series ring $k\left[\right[t\left]\right]$ over a perfect field $k$ of positive characteristic. Let $D$ be the associated formal mixed-characteristic deformation functor. Assume that the action of $G$ is weakly ramified, i.e., the second ramification group is trivial. Example: for a group action on an ordinary curve, the action of a ramification group on the completed local ring of any point is weakly ramified.We prove that the only such $D$ that are not pro-representable...