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Abstract Charged-particle trajectories are usually reconstructed with the LHCb detector using combined information from the tracking devices placed upstream and downstream of the 4 T m 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. The challenges of the reconstruction of long-lived particles with T tracks for physics use are discussed and solutions are proposed. The feasibility and the tracking performance are studied using samples of long-lived$${\Lambda }$$ $\Lambda$and$$K_S^0$$ $K_S^0$hadrons decaying between 6.0 and 7.6 m downstream of the proton–proton collision point, thereby traversing most of the magnetic field region and providing maximal sensitivity to magnetic and electric dipole moments. The reconstruction can be expanded upstream to about 2.5 m for use in direct searches of exotic long-lived particles. The data used in this analysis have been recorded between 2015 and 2018 and correspond to an integrated luminosity of 6 $$\hbox {fb}^{-1}$$ ${\text{fb}}^{-1}$. The results obtained demonstrate the possibility to further extend the decay volume and the physics reach of the LHCb experiment.