Invariance of the Hard Lefschetz condition for compact completely solvable manifolds

Let $M$ be a compact completely solvable manifold, and let $\omega$ be a symplectic structure on $M$. The Hard Lefschetz invariance conjecture. If $\omega$ satisfies the Hard Lefschetz condition (HLC), then every other symplectic structure on $M$ also satisfies the HLC. The conjecture proposes that, on a compact completely solvable manifold, the HLC is a property of the manifold rather than of the chosen symplectic structure. The paper verifies this for the compact completely solvable manifolds considered there, but the general assertion remains open.