We present kpc-scale ALMA and HST imaging of the quasar PJ308-21 at $z$=$6.2342$, tracing dust, gas (via the [CII] 158 $mu$m line) and young stars. At a resolution of $sim0.3$ ($approx1.7$ kpc), the system is resolved over $>4$ ($>$20 kpc). In particular, it features a main component, identified to be the quasar host galaxy, centered on the accreting supermassive black hole; and two other extended components on the West and East side, one redshifted and the other blueshifted relative to the quasar. The [CII] emission of the entire system stretches over $>$1500 km/s along the line of sight. All the components of the system are observed in dust, [CII], and rest-frame UV emission. The inferred [CII] luminosities [(0.9-4.6)$times 10^9$ L$_odot$], dust luminosities [(0.15-2.6)$times10^{12}$ L$_odot$], and rest-frame UV luminosities [(6.6-15)$times10^{10}$ L$_odot$], their ratios, and the implied gas/dust masses and star formation rates [11-290 M$_odot$ yr$^{-1}$] are typical of high-redshift star-forming galaxies. A toy model of a single satellite galaxy that is tidally stripped by the interaction with the quasar host galaxy can account for the observed velocity and spatial extent of the two extended components. An outflow interpretation of the unique features in PJ308-21 is not supported by the data. PJ308-21 is thus one of the earliest galaxy mergers imaged at cosmic dawn.