The lifting conjecture for exact equivariant Morita classes

Let $H$ be a finite-dimensional Hopf algebra with the dual Chevalley property, let $H_0$ be its coradical, and let $X_0$ be a complete set of exact $H_0$-equivariant Morita equivalence class representatives. Then define

$$X:=\left\{A: \lambda^{-1}(H_0\otimes A)\text{ is isomorphic to an element in }X_0\right\}.$$

Lifting conjecture. The set $X$ is a complete set of exact $H$-equivariant Morita equivalence class representatives.

This conjecture proposes that exact equivariant Morita equivalence classes for a finite-dimensional Hopf algebra with the dual Chevalley property can be classified by lifting representatives from the coradical. It is motivated by the lifting method and computations for pointed Hopf algebras with cyclic coradical; the supplied source gives no resolution.