We used the COSMOS2020 catalog to measure the stellar-to-halo mass relation (SHMR) divided by central and satellite galaxies from z = 0.2 to z = 5.5. Starting from accurate photometric redshifts, we measured the near-infrared selected two-point angular correlation and stellar mass functions in ten redshift bins. We used a phenomenological model that parametrizes the stellar-to- halo mass relation for central galaxies and the number of galaxies inside each halo to describe our observations. This model qualitatively reproduces our measurements and their dependence on the stellar mass threshold. Surprisingly, the mean halo occupation distribution only shows a mild evolution with redshift suggesting that galaxies occupy halos similarly throughout cosmic time. At each redshift, we measured the ratio of stellar mass to halo mass, M$_$/M$_h$, which shows the characteristic strong dependence of halo mass with a peak at M$_h$$^peak$ ensuremath∼ 2 × 10$^12$ M$_ensuremathødot$. For the first time, using a joint modeling of clustering and abundances, we measured the evolution of M$_h$$^peak$ from z = 0.2 to z = 5.5. M$_h$$^peak$ increases gradually with redshift from log M$_h$$^peak$/M$_ensuremathødot$ ensuremath∼ 12.1 at z ensuremath∼ 0.3 to log M$_h$$^peak$/M$_ensuremathødot$ ensuremath∼ 12.3 at z ensuremath∼ 2, and up to log M$_h$$^peak$/M$_ensuremathødot$ ensuremath∼ 12.9 at z ensuremath∼ 5. Similarly, the stellar mass peak M$_ensuremath$$^peak$ increases with redshift from log M$_ensuremath*$$^peak$/M$_ensuremathødot$ ensuremath∼ 10.5 at z ensuremath∼ 0.3 to log M$_ensuremath*$$^peak$/M$_ensuremathødot$ ensuremath∼ 10.9 at z ensuremath∼ 3. The SHMR ratio at the peak halo mass remains almost constant with redshift. These results are in accordance with the scenario in which the peak of star-formation efficiency moves toward more massive halos at higher redshifts. We also measured the fraction of satellites as a function of stellar mass and redshift. For all stellar mass thresholds, the satellite fraction decreases at higher redshifts. At a given redshift, there is a higher fraction of low-mass satellites and this fraction reaches a plateau at ensuremath∼25% at z ensuremath∼ 1. The satellite contribution to the total stellar mass budget in halos becomes more important than that of the central at halo masses of about M$_h$ > 10$^13$ M$_ensuremathødot$ and always stays below the peak, indicating that quenching mechanisms are present in massive halos that keep the star- formation efficiency low. Finally, we compared our results with three hydrodynamical simulations: HORIZON-AGN, TNG100 of the ILLUSTRISTNG project, and EAGLE. We find that the most significant discrepancy is at the high-mass end, where the simulations generally show that satellites have a higher contribution to the total stellar mass budget than the observations. This, together with the finding that the fraction of satellites is higher in the simulations, indicates that the feedback mechanisms acting in both group- and cluster-scale halos appear to be less efficient in quenching the mass assembly of satellites - and that quenching occurs much later in the simulations.