We study linear, conservative, stationary dynamical systems (l.c.s.d.s)
with unbounded main operator and their transfer operator-valued functions. A new
class of transfer operator-valued functions is introduced and shown that this class is
invariant with respect to multiplication (from the left, from the right or both) by a
constant J-unitary operator. The problem how to realize the product W(z)B as a
transfer function of some l.c.s.d.s with an arbitrary J-unitary operator B and given
realization of W(z) is considered.