  There are well known relations between braid groups and symmetric groups,
between Artin-Briskorn braid groups and Coxeter groups. Inverse braid monoid
the same way is related to the inverse symmetric monoid. In the paper we show
that similar relations exist between the inverse braid monoid of type $B$ and
the inverse reflection monoid of type $B$. This gives a presentation of the
last monoid.
