  Besides being important to determine Standard Model parameters such as the
CKM matrix elements $|V_{cb}|$ and $|V_{ub}|$, semileptonic $B$ decays seem
also promising to reveal new physics (NP) phenomena, in particular in
connection with the possibility of uncovering lepton flavour universality (LFU)
violating effects. In this view, it could be natural to connect the tensions in
the inclusive versus exclusive determinations of $|V_{cb}|$ to the anomalies in
the ratios $R(D^{(*)})$ of decay rates into $\tau$ vs $\mu, e$. However, the
question has been raised about the role of the parametrization of the hadronic
$B \to D^{(*)}$ form factors in exclusive $B$ decay modes. We focus on the
fully differential angular distributions of $\bar B \to D^* \ell^-{\bar
\nu}_\ell$ with $D^* \to D \pi$ or $D^* \to D \gamma$, the latter mode being
important in the case of $B_s \to D_s^*$ decays. We show that the angular
coefficients in the distributions can be used to scrutinize the role of the
form factor parametrization and to pin down deviations from SM. As an example
of a NP scenario, we include a tensor operator in the $b \to c$ semileptonic
effective Hamiltonian, and discuss how the angular coefficients allow to
construct observables sensitive to this structure, also defining ratios useful
to test LFU.
