  We show a canonical injective morphism from the quantum cohomology ring
QH(G/P) to the associated graded algebra of QH(G/B), which is with respect to a
nice filtration on QH(G/B) introduced by Leung and the author. This tells us
the vanishing of a lot of genus zero, three-pointed Gromov-Witten invariants of
flag varieties G/P.
