  The $\bar{B}\to D^{*+} l^-\bar{\nu}_{l}$ branching fraction ratio $R(D^{*})$
has shown intriguing discrepancies between the Standard Model prediction and
measurements performed at BaBar, Belle and LHCb experiments, a possible sign of
beyond the Standard Model physics. Theoretical studies prove how observables
related to the $\bar{B}\to D^{*+} l^-\bar{\nu}_{l}$ differential decay
distribution can be used to further constrain New Physics contributions, but
their experimental measurements is lacking to date. This article presents the
attainable precision on the measurement of $\bar{B}\to D^{*+} l^-\bar{\nu}_{l}$
angular and CP-violating observables by exploiting approximate reconstruction
algorithms using information from detectable final-state particles only, a case
of special interest for hadron collider experiments. The resolution on the
phase space variables is studied using $\bar{B}\to D^{*+} l^-\bar{\nu}_{l}$
decays simulated in a forward detector geometry like LHCb. A novel method to
correct the observable values for the reconstruction inaccuracies based on
detector simulation is successfully tested on simulated data and the decrease
in precision with respect to a perfect reconstruction is evaluated. The
$D^{*+}$ longitudinal polarization fraction and one of the CP-violating
observables can be measured losing a factor 2 and 5 in precision, respectively.
The extraction of phase space distributions from the template fit selecting
$\bar{B}\to D^{*+} l^-\bar{\nu}_{l}$ decays and associated systematic
uncertainties are also discussed.
