  We investigate the influence of Br$^-$/S$^{2-}$ site-exchange on lithium
diffusion in the agyrodite-type solid electrolyte Li$_6$PS$_5$Br by ab-initio
molecular dynamics simulations. Based on the calculated trajectories a new
mechanism for the internal lithium reorganization within the Li-cages around
the $4d$ sites is identified. This reorganization mechanism is highly concerted
and cannot be described by one single rotation axis only. Simulations with
Br$^-$/S$^{2-}$ defects reveal that Li$^._i$ interstitials are the dominant
mobile charge carriers, which originate from Frenkel pairs. These are formed
because Br$^._\text{S}$ defects on the $4d$ sites cause the transfer of one or
even two Li$^._i$ to the neighboring 12 cages. The lithium interstitials then
carry out intercage jumps via interstitial and interstitialcy mechanisms. With
that, one single Br$^._\text{S}$ defect enables Li diffusion over an extended
spatial area explaining why low degrees of site-exchange are sufficient to
trigger superionic conduction. The vacant sites of the Frenkel pairs, namely
V$'_\text{Li}$, are mostly immobile and bound to the Br$^._\text{S}$ defect. To
a lesser degree also S$'_\text{Br}$ defects induce disturbances in the lithium
distribution and act as sinks for lithium interstitials restricting the
Li$^._i$ motion to the vicinity of the S$'_\text{Br}$ defect.
