We present an updated event generator THESEUS, based on the three-fluid dynamics (3FD), complemented by UrQMD cascade for the late stage of the nuclear collision. The generator is extended to simulate light-nuclei production in relativistic heavy-ion collisions via thermal mechanism, on the same basis as hadrons. We present the rapidity, transverse momentum spectra, first v$_1$ flow harmonics of deuterons, tritons, $^3$He at different collision energies and impact parameters. The results are compared with experimental data from NA49 and STAR. We show that anti-deuteron spectra from THESEUS are in agreement with STAR data. We demonstrate the contributions from the excited states of Helium to the yields of deuteron, triton and $^3$He. The reproduction is achieved without any extra parameters, while the original coalescence approach in 3FD requires a tuning of the coalescence coefficients for each light nucleus separately.