  Charged-particle trajectories are usually reconstructed with the LHCb
detector using combined information from the tracking devices placed upstream
and downstream of the 4 Tm dipole magnet. Trajectories reconstructed using only
information from the tracker downstream of the dipole magnet, which are
referred to as T tracks, have not been used for physics analysis to date due to
their limited momentum resolution. The challenges of the reconstruction of
long-lived particles using T tracks for use in physics analyses are discussed
and a solution is proposed. The feasibility of the experimental technique is
demonstrated by reconstructing samples of long-lived $\it \Lambda$ and $K_S^0$
hadrons decaying between 6.0 and 7.6 metres downstream of the proton-proton
collision point. The long-lived hadrons are selected using a data sample
recorded between 2015 and 2018, corresponding to an integrated luminosity of
about 6 fb$^{-1}$. These results open an opportunity to further extend the
physics reach of the LHCb experiment.
