  For an arbitrary smooth hypersurface X in a projective space, we construct
its LG moduli of quasimaps with P fields. Apply Kiem-Li's cosection
localization we obtain a virtual fundamental class. We show the class
coincides, up to sign, with that of moduli of quasimaps to X. This generalizes
Chang-Li's numerical identity to the cycle level, and from Gromov Witten
invariants to quasimap invariants.
