  Dynamical interactions involving binaries play a crucial role in the
evolution of star clusters and galaxies. We continue our investigation of the
hydrodynamics of three-body encounters, focusing on binary black hole (BBH)
formation, stellar disruption, and electromagnetic (EM) emission in dynamical
interactions between a BH-star binary and a stellar-mass BH, using the
moving-mesh hydrodynamics code {\small AREPO}. This type of encounters can be
divided into two classes depending on whether the final outcome includes BBHs.
This outcome is primarily determined by which two objects meet at the first
closest approach. BBHs are more likely to form when the star and the incoming
BH encounter first with an impact parameter smaller than the binary's semimajor
axis. In this case, the star is frequently disrupted. On the other hand, when
the two BHs encounter first, frequent consequences are an orbit perturbation of
the original binary or a binary member exchange. For the parameters chosen in
this study, BBH formation, accompanied by stellar disruption, happens in
roughly 1 out of 4 encounters. The close correlation between BBH formation and
stellar disruption has possible implications for EM counterparts at the
binary's merger. The BH that disrupts the star is promptly surrounded by an
optically and geometrically thick disk with accretion rates exceeding the
Eddington limit. If the debris disk cools fast enough to become long-lived, EM
counterparts can be produced at the time of the BBH merger.
