  This paper generalizes the results obtained in an earlier paper
(math.OA/0003087) for finite factors to infinite but still semifinite factors.
First we give a characterization of cyclic and separating vectors for infinite
semifinite factors in terms of operators associated with this vector and being
affiliated with the factor. Further we show how this operator generates the
modular objects of the given cyclic and separating vector generalizing an idea
of Kadison and Ringrose. With the help of these results we can show that the
second simple class of solutions for the inverse problem constructed in
math.OA/0003087 never exists in infinite semifinite factors. Finally we give a
classification of the solutions of the inverse problem in the case of modular
operators having pure point spectrum, completely analoguous to the finite case.
