FAUST XI: Enhancement of the complex organic material in the shocked matter surrounding the [BHB2007] 11 protobinary system

iCOMs are species commonly found in the interstellar medium. They are believed to be crucial seed species for the build-up of chemical complexity in star forming regions as well as our own Solar System. Thus, understanding how their abundances evolve during the star formation process and whether it enriches the emerging planetary system is of paramount importance. We use data from the ALMA Large Program FAUST to study the compact line emission towards the [BHB2007] 11 proto-binary system (sources A and B), where a complex structure of filaments connecting the two sources with a larger circumbinary disk has previously been detected. More than 45 CH3OCHO lines are clearly detected, as well as 8 CH3OCH3 transitions , 1 H2CCO transition and 4 t-HCOOH transitions. We compute the abundance ratios with respect to CH3OH for CH3OCHO, CH3OCH3, H2CCO, t-HCOOH (as well as an upper limit for CH3CHO) through a radiative transfer analysis. We also report the upper limits on the column densities of nitrogen bearing iCOMs, N(C2H5CN) and N(C2H3CN). The emission from the detected iCOMs and their precursors is compact and encompasses both protostars, which are separated by only 0.2" (~ 28 au). The integrated intensities tend to align with the Southern filament, revealed by the high spatial resolution observations of the dust emission at 1.3 mm. A PV and 2D analysis are performed on the strongest and uncontaminated CH3OCH3 transition and show three different spatial and velocity regions, two of them being close to 11B (Southern filament) and the third one near 11A. All our observations suggest that the detected methanol, as well as the other iCOMs, are generated by the shocked gas from the incoming filaments streaming towards [BHB2007] 11A and 11B, respectively, making this source one of the few where chemical enrichment of the gas caused by the streaming material is observed.