  The quark rearrangement model for baryon-antibaryon annihilation and
reproduction ($B\bar B\leftrightarrow 3M$) - incorporated in the
Parton-Hadron-String Dynamics (PHSD) transport approach - is extended to the
strangeness sector. A derivation of the transition probabilities for the
three-body processes is presented and a strangeness suppression factor for the
invariant matrix element squared is introduced to account for the higher mass
of the strange quark compared to the light up and down quarks. In simulations
of the baryon-antibaryon annihilation and reformation in a box with periodic
boundary conditions we demonstrate that our numerical implementation fulfills
detailed balance on a channel-by-channel basis for more than 2000 individual $2
\leftrightarrow 3$ channels. Furthermore, we study central Pb+Pb collisions
within PHSD from 11.7$A$ GeV to 158$A$ GeV and investigate the impact of the
additionally implemented reaction channels in the strangeness sector. We find
that the new reaction channels have a visible impact essentially only on the
rapidity spectra of antibaryons. The spectra with the additional channels in
the strangeness sector are closer to the experimental data than without for all
antihyperons. Due to the chemical redistribution between baryons/antibaryons
and mesons we find a slightly larger production of antiprotons thus moderately
overestimating the available experimental data. We additionally address the
question if the antibaryon spectra (with strangeness) from central heavy-ion
reactions at these energies provide further information on the issue of chiral
symmetry restoration and deconfinement. However, by comparing transport results
with/without partonic phase as well as including/excluding effects from chiral
symmetry restoration we find no convincing signals in the strange antibaryon
sector for either transition due to the strong final-state interactions.
