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The ALMA interferometer has played a key role in revealing a new component of the Sun-like star forming process: the molecular streamers, i.e. structures up to thousands of au long funneling material non-axisymmetrically to disks. In the context of the FAUST ALMA LP, the archetypical VLA1623-2417 protostellar cluster has been imaged at 1.3 mm in the SO(5$_6$--4$_5$), SO(6$_6$--5$_5$), and SiO(5--4) line emission at the spatial resolution of 50 au. We detect extended SO emission, peaking towards the A and B protostars. Emission blue-shifted down to 6.6 km s$^{-1}$ reveals for the first time a long ($\sim$ 2000 au) accelerating streamer plausibly feeding the VLA1623 B protostar. Using SO, we derive for the first time an estimate of the excitation temperature of an accreting streamer: 33$\pm$9 K. The SO column density is $\sim$ 10$^{14}$ cm$^{-2}$, and the SO/H$_2$ abundance ratio is $\sim$ 10$^{-8}$. The total mass of the streamer is 3 $\times$ 10$^{-3}$ $Msun$, while its accretion rate is 3--5 $\times$ 10$^{-7}$ Msun yr$^{-1}$. This is close to the mass accretion rate of VLA1623 B, in the 0.6--3 $\times$ 10$^{-7}$ Msun yr$^{-1}$ range, showing the importance of the streamer in contributing to the mass of protostellar disks. The highest blue- and red-shifted SO velocities behave as the SiO(5--4) emission, the latter species detected for the first time in VLA1623-2417: the emission is compact (100-200 au), and associated only with the B protostar. The SO excitation temperature is $\sim$ 100 K, supporting the occurrence of shocks associated with the jet, traced by SiO., Comment: accepted by MNRAS