Top: Two epochs of GTC/EMIR J-band images of BD+02°3375 in logarithm count scale. The positions of the comoving companion candidate are pointed out by red arrows. The motion is not visible in the difference image of Fig. B.1. Bottom: Proper motion diagram of the sources. The proper motion of the primary (red cross) agrees well with Gaia (red star) within the uncertainties. The background sources extracted by daofind and by hand have almost zero proper motion (black dots). The candidate (blue cross) has a significant proper motion compared to the background sources, but is not comoving with the primary.