  We investigate the decay of $\bar B^0 \to \bar K^{*0} R$ and $\bar B^0_s \to
\phi R$ with $R$ being the $X(4160)$, $Y(3940)$, $Z(3930)$ resonances. Under
the assumption that these states are dynamically generated from the
vector-vector interaction, as has been concluded from several theoretical
studies, we use a reaction mechanism of quark production at the elementary
level, followed by hadronization of one final $q \bar q$ pair into two vectors
and posterior final state interaction of this pair of vector mesons to produce
the resonances. With this procedure we are able to predict five ratios for
these decays, which are closely linked to the dynamical nature of these states,
and also predict the order of magnitude of the branching ratios which we find
of the order of $10^{-4}$, well within the present measurable range. In order
to further test the dynamical nature of these resonances we study the $\bar
B^0_s \to \phi D^* \bar D^*$ and $\bar B^0_s \to \phi D_s^* \bar D_s^*$ decays
close to the $D^* \bar D^*$ and $D_s^* \bar D_s^*$ thresholds and make
predictions for the ratio of the mass distributions in these decays and the
$\bar B^0_s \to \phi R$ decay widths. The measurement of these decays rates can
help unravel the nature of these resonances.
