  The first detections of black hole - neutron star mergers (GW200105 and
GW200115) by the LIGO-Virgo-Kagra Collaboration mark a significant scientific
breakthrough. The physical interpretation of pre- and post-merger signals
requires careful cross-examination between observational and theoretical
modelling results. Here we present the first set of black hole - neutron star
simulations that were obtained with the numerical-relativity code BAM. Our
initial data are constructed using the public LORENE spectral library which
employs an excision of the black hole interior. BAM, in contrast, uses the
moving-puncture gauge for the evolution. Therefore, we need to ``stuff'' the
black hole interior with smooth initial data to evolve the binary system in
time. This procedure introduces constraint violations such that the constraint
damping properties of the evolution system are essential to increase the
accuracy of the simulation and in particular to reduce spurious center-of-mass
drifts. Within BAM we evolve the Z4c equations and we compare our
gravitational-wave results with those of the SXS collaboration and results
obtained with the SACRA code. While we find generally good agreement with the
reference solutions and phase differences $\lesssim 0.5$ rad at the moment of
merger, the absence of a clean convergence order in our simulations does not
allow for a proper error quantification. We finally present a set of different
initial conditions to explore how the merger of black hole neutron star systems
depends on the involved masses, spins, and equations of state.
