  A version of mirror symmetry predicts a ring isomorphism between quantum
cohomology of a symplectic manifold and Jacobian algebra of the Landau-Ginzburg
mirror, and for toric manifolds Fukaya-Oh-Ohta-Ono constructed such a map
called Kodaira-Spencer map using Lagrangian Floer theory. We discuss a general
construction of Kodaira-Spencer ring homomorphism when LG mirror potential $W$
is given by $J$-holomorphic discs with boundary on a Lagrangian $L$: we find an
$A_{\infty}$-algebra $\mathcal{B}$ whose $m_1$-complex is a Koszul complex for
$W$ under mild assumptions on $L$. Closed-open map gives a ring homomorphism
from quantum cohomology to cohomology algebra of $\mathcal{B}$ which is
Jacobian algebra of $W$.
  We also construct an equivariant version for orbifold LG mirror $(W,H)$. We
construct a Kodaira-Spencer map from quantum cohomology to another
$A_{\infty}$-algebra $(\mathcal{B}\rtimes H)^H$ whose cohomology algebra is
isomorphic to the orbifold Jacobian algebra of $(W,H)$ under an assumption. For
the $2$-torus whose mirror is an orbifold LG model given by Fermat cubic with a
$\mathbb{Z}/3$-action, we compute an explicit Kodaira-Spencer isomorphism.
