  This is the second of a sequence of papers proving the quantum invariance for
ordinary flops over an arbitrary smooth base. In this paper, we complete the
proof of the invariance of the big quantum rings under ordinary flops of
splitting type.
  To achieve that, several new ingredients are introduced. One is a quantum
Leray--Hirsch theorem for the local model (a certain toric bundle) which
extends the quantum D module of Dubrovin connection on the base by a
Picard--Fuchs system of the toric fibers.
  Nonsplit flops as well as further applications of the quantum Leray--Hirsch
theorem will be discussed in subsequent papers. In particular, a quantum
splitting principle is developed in Part III which reduces the general ordinary
flops to the split case solved here.
