  This paper revisits the partial information optimal control problem
considered by Wang, Wu and Xiong [Wang et al 2013], where the system is derived
by a controlled forward-backward stochastic differential equation with
correlated noises between the system and the observation.
  For this type of partial information optimal control problem, one necessary
and one suffcient (a verification theorem) conditions of optimality are derived
using a unified way.
  We improve the $L^p-$ bounds on the control from $L^8$ in [Want et al 2013]
to $L^4$ in this paper.
