Morita autoequivalence conjecture for Weyl algebras

Let $A_{n,\mathbb C}$ be the Weyl algebra of index $n$ over $\mathbb C$, and let $P_{n,\mathbb C}$ be the Poisson algebra of polynomial functions on the $2n$-dimensional affine symplectic space. Morita autoequivalence conjecture. The group of Morita autoequivalences of $A_{n,\mathbb C}$ is isomorphic to the group of polynomial symplectomorphisms:

$$\operatorname{MoritaAut}(A_{n,\mathbb C})\simeq \operatorname{Aut}(P_{n,\mathbb C}).$$

The paper presents this as a weaker version of the Weyl–Poisson automorphism conjecture, potentially surviving even if the corresponding bimodules are not free. The supplied source gives no resolution.