Common proper-motion test of the companion candidate around LSPM J1514+6433. The first and second epochs correspond to the Robo-AO observation (Lamman et al. 2020) and the IRD-FIM observation dates, respectively. The expected position corresponds to the simulated position assuming a background star with zero proper motion on the IRD observation date based on the first position. The green line indicates the trajectory of the simulated motion of the background star. We also assumed a zero proper-motion acceleration for the primary star induced by the companion.