Context. Recent observations suggest that planet formation starts early, in protostellar disks of ≤105 yr, which are characterized by strong interactions with the environment, such as through accretion streamers and molecular outflows.Aims. To investigate the impact of such phenomena on the physical and chemical properties of a disk, it is key to understand what chemistry planets inherit from their natal environment. Methods. In the context of the ALMA large program Fifty AU Study of the chemistry in the disk/envelope system of solar-like protostars (FAUST), we present observations on scales from ∼1500 au to ∼60 au of H2CO, HDCO, and D2CO toward the young planet-forming disk IRS 63. Results. The H2CO probes the gas in the disk as well as in a large scale streamer (∼1500 au) impacting onto the southeast disk side. We detected for the first time deuterated formaldehyde, HDCO and D2CO, in a planet-forming disk and HDCO in the streamer that is feeding it. These detections allowed us to estimate the deuterium fractionation of H2CO in the disk: [HDCO]/[H2CO] ∼ 0.1 − 0.3 and [D2CO]/[H2CO] ∼ 0.1. Interestingly, while HDCO follows the H2CO distribution in the disk and in the streamer, the distribution of D2CO is highly asymmetric, with a peak of the emission (and [D]/[H] ratio) in the southeast disk side, where the streamer crashes onto the disk. In addition, D2CO was detected in two spots along the blue- and redshifted outflow. This suggests that (i) in the disk, HDCO formation is dominated by gas-phase reactions in a manner similar to H2CO, while (ii) D2CO is mainly formed on the grain mantles during the prestellar phase and/or in the disk itself and is at present released in the gas phase in the shocks driven by the streamer and the outflow. Conclusions. These findings testify to the key role of streamers in the buildup of the disk concerning both the final mass available for planet formation and its chemical composition.