  We present an updated determination of the values of $\vert V_{cb} \vert$,
$R(D^*)$ and $\vert V_{ub} \vert/\vert V_{cb} \vert$ based on the new data on
semileptonic $B \to D^* \ell \nu_\ell$ decays by the Belle and Belle-II
Collaborations and on the recent theoretical progress in the calculation of the
form factors relevant for semileptonic $B \to D^* \ell \nu_\ell$ and $B_s \to K
\ell \nu_\ell$ decays. In particular we present results derived by applying
either the Dispersive Matrix (DM) method of Refs. [1-6] or the more standard
Boyd-Grinstein-Lebed (BGL) [7] approach to the most recent values of the form
factors determined in lattice QCD. Using all the available lattice results for
the form factors from the DM method we get the theoretical value $R^{\rm
th}(D^*) = 0.262 \pm 0.009$ and we extract from a bin-per-bin analysis of the
experimental data the value $\vert V_{cb} \vert = (39.92 \pm 0.64)
\cdot10^{-3}$. Our result for $R(D^*)$ is consistent with the latest
experimental world average $R^{\rm exp}(D^*) = 0.284 \pm 0.012$ [8]} at the
$\simeq 1.5\,\sigma$ level. Our value for $\vert V_{cb} \vert$ is compatible
with the latest inclusive determinations $\vert V_{cb} \vert^{\rm incl} =
(41.97 \pm 0.48) \cdot 10^{-3}$ [9] and $\vert V_{cb} \vert^{\rm incl} =
(41.69\pm 0.63) \cdot 10^{-3}$ [10] within $\simeq 2.6$ and $\simeq 2.0$
standard deviations, respectively. From a reappraisal of the calculations of
$\vert V_{ub} \vert / \vert V_{cb} \vert$, we also obtain $\vert V_{ub} \vert /
\vert V_{cb} \vert = 0.087\pm 0.009$ in good agreement with the result $\vert
V_{ub} \vert / \vert V_{cb} \vert = 0.0844\pm 0.0056$ from the latest FLAG
review [11].
