  Boxy/peanut bulges are believed to originate from galactic discs through
secular processes. A little explored question is how this evolution would be
modified if the initial disc was assembled around a preexisting classical
bulge. Previously we showed that a low-mass initial classical bulge (ICB), as
might have been present in Milky Way-like galaxies, can spin up significantly
by gaining angular momentum from a bar formed through disc instability. Here we
investigate how the disc instability and the kinematics of the final
boxy/peanut (BP) bulge depend on the angular momentum of such a low-mass ICB.
We show that a strong bar forms and transfers angular momentum to the ICB in
all our models. However, rotation in the ICB limits the emission of the bar's
angular momentum, which in turn changes the size and growth of the bar, and of
the BP bulge formed from the disc.
  The final BP bulge in these models is a superposition of the BP bulge formed
via the buckling instability and the spun-up ICB. We find that the long-term
kinematics of the composite BP bulges in our simulations is independent of the
rotation of the ICB, and is always described by cylindrical rotation. However,
as a result of the co-evolution between bulge and bar, deviations from
cylindrical rotation are seen during the early phases of secular evolution, and
may correspond to similar deviations observed in some bulges. We provide a
simple criterion to quantify deviations from pure cylindrical rotation, apply
it to all our model bulges, and also illustrate its use for two galaxies:
NGC7332 and NGC4570.
