We report the discovery of Serenity-18, a galaxy at z=5.939 for which we could measure the content of molecular gas, M(H_2)~ 5 x10^9 M_sun, traced by the CO(6-5) emission, together with the metal-poor ([Fe/H]=-3.08 +- 0.12, [Si/H]=-2.86 +- 0.14) gas clump/filament which is possibly feeding its growth. The galaxy has an estimated star formation rate of ~100 M_sun yr^{-1}, implying that it is a typical main sequence galaxy at these redshifts. The metal-poor gas is detected through a damped Lyman-alpha absorber (DLA) observed at a spatial separation of 40 kpc and at the same redshift of Serenity-18, along the line of sight to the quasar SDSS J2310+1855 (z_em = 6.0025). The chemical abundances measured for the damped Lyman-alpha system are in very good agreement with those measured for other DLAs discovered at similar redshifts, indicating an enrichment due to massive PopII stars. The galaxy/Damped system we discovered is a direct observational evidence of the assembly of a galaxy at the edge of the reionization epoch.