Fukaya's cohomology F-manifold mirror symmetry conjecture

Let $M$ and $M^{\vee}$ be open Calabi–Yau manifolds that are mirror to each other in the sense of homological mirror symmetry. Write $SH^*(M)$ for the symplectic cohomology of $M$, and let $H^*(M^{\vee},\bigwedge^*T_{M^{\vee}})$ denote the cohomology of polyvector fields on $M^{\vee}$. Fukaya's cohomology F-manifold mirror symmetry conjecture. The ring isomorphism

$$SH^*(M)\cong H^*(M^{\vee},\bigwedge^*T_{M^{\vee}})$$

can be lifted to an isomorphism of cohomology F-manifolds. This is an expected enhancement of homological mirror symmetry: it requires compatibility not only with the ring structures but with the higher cohomology F-manifold structures. The supplied text does not state whether this conjecture has been proved or disproved.