Frobenius manifold formulation of Fourier-Mukai duality

I would like to know if there exists a formulation/incarnation of the Fourier-Mukai duality in terms of the corresponding Frobenius manifold constructed by Barannikov and Kontsevich: http://arxiv.org/pdf/alg-geom/9710032

Damien

Anyway in short, the derived category (or better an enhanced, dg or $A_\infty$) version controls all the other aspects of the B-model TFT, so all the other constructions in mirror symmetry on the B-side can be recovered intrinsically from it (and are therefore invariant under derived equivalence).