Generalized deformation invariance conjecture for 2-step nilmanifolds

Let $M$ be a 2-step nilmanifold with abelian complex structure. Suppose that there exists an ascending basis

$$\{\omega^1,\dots,\omega^{n+1}\}$$

such that $d\omega^{n+1}$ is non-degenerate. Let $\Gamma_1\in H^2(M)$ be integrable to a generalized deformation $\Gamma$. Generalized deformation invariance conjecture. The Gerstenhaber algebra

$$\left(H^\bullet_{\Gamma}(M),\lbrack\!\lbrack-, -\rbrack\!\rbrack,\wedge\right)$$

is naturally isomorphic to

$$\left(H^\bullet(M),\lbrack\!\lbrack-, -\rbrack\!\rbrack,\wedge\right).$$

The conjecture extends the observed invariance of holomorphic Poisson cohomology to generalized deformations on a large class of 2-step nilmanifolds with abelian complex structures. The supplied text does not state whether it is open or resolved.