  In the framework of HQET inclusive decays of b-flavored hadrons can be
handled as decays of the free b-quark approximately. We analyse the correction
to this approximation for the inclusive decays into a polarized $J/\psi$,the
correction is characterized by two matrix elements defined in HQET. For the
$J/\psi$ we use NRQCD to parameterize the formation of the $c\bar c$ pair into
$J/\psi$. Numerically the correction is remarkably large, it can be at the
level of 30% and it is mainly due to the Fermi-motion of the $b$-quark. With
this correction we give a new determination for combinations of two NRQCD
matrix elements.
