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Context. Deuterium in H-bearing species is enhanced during the early stages of star formation, however, only a small number of high spatial resolution deuteration studies exist towards protostellar objects, leaving the small-scale structures unrevealed and understudied. Aims. We aim to constrain the deuterium fractionation ratios in a Class 0/I protostellar object in formaldehyde (H2CO), which has abundant deuterated isotopologues in this environment. Methods. We observed the Class 0/I protobinary system [BHB2007] 11, whose emission components are embedded in circumstellar disks that have radii of 2-3 au, using ALMA within the context of the Large Program FAUST. The system is surrounded by a complex filamentary structure connecting to the larger circumbinary disk. In this work we present the first study of formaldehyde D-fractionation towards this source with detections of H2CO 3(0,3)-2(0,2), combined with HDCO 4(2,2)-3(2,1), HDCO 4(1,4)-3(1,3) and D2CO 4(0,4)-3(0,3). These observations enable multiple velocity components associated with the methanol hotspots also uncovered by FAUST data, as well as the external envelope, to be resolved. In addition, based on the kinematics seen in the observations of the H2CO emission, we propose the presence of a second large scale outflow. Results. HDCO and D2CO are only found in the central regions of the core while H2CO is found more ubiquitously. From radiative transfer modelling, the column densities ranges found for H2CO, HDCO and D2CO are (3-8)x10$^{14}$ cm$^{-2}$, (0.8-2.9)x10$^{13}$ cm$^{-2}$ and (2.6-4.3)x10$^{12}$ cm$^{-2}$, respectively, yielding an average D/H ratio of 0.01-0.04. Following the results of kinematic modelling, the second large scale feature is inconsistent with a streamer-like nature and we thus tentatively conclude that the feature is an asymmetric molecular outflow launched by a wide-angle disk wind., Comment: 17 pages, 15 figures