  Finding tracks downstream of the magnet at the earliest LHCb trigger level is
not part of the baseline plan of the upgrade trigger, on account of the
significant CPU time required to execute the search. Many long-lived particles,
such as $K^0_S$ and strange baryons, decay after the vertex track detector, so
that their reconstruction efficiency is limited. We present a study of the
performance of a future innovative real-time tracking system based on FPGAs,
developed within a R\&D effort in the context of the LHCb Upgrade Ib (LHC
Run~4), dedicated to the reconstruction of the particles downstream of the
magnet in the forward tracking detector (Scintillating Fibre Tracker), that is
capable of processing events at the full LHC collision rate of 30 MHz.
