  We calculate the process- and polarization-dependent nonfactorizable terms
$+AFw-widetilde{a}_{+AFw-lambda}$ of the B$+AFw-to$ J$/+AFw-Psi {+AFw-rm K^*}$
decay within the QCD-improved factorization approach. The longitudinal part
$+AFw-widetilde{a}_{0}$ is infrared convergent and large enough to agree with
recent experimental data, provided that the B-K$^*$ form factors
$A_1(m^2_{+AFw-Psi})$ and $A_2(m^2_{+AFw-Psi})$ satisfy some constraints met by
many (but not all) models.
  The transverse parts $+AFw-widetilde{a}_{+AFw-pm}$ on the other hand are
infrared divergent, the procedure used to handle such divergence is discussed
in relation with the B$+AFw-to$ J$/+AFw-Psi {+AFw-rm K}$ case in which the same
problem arises. Our nonzero phases of the helicity amplitudes are consistent
with experimental data recently measured for the first time by the BaBar
collaboration.
