The dynamics of a pair of identical artificial microswimmers bound inside two harmonic traps, in a thin sheared fluid film, is numerically investigated. In a two-dimensional Oseen approximation, the hydrodynamic pair coupling is long-ranged and proportional to the particle radius to film thickness ratio. On increasing such ratio above a certain threshold, a transition occurs between a free regime, where each swimmer orbits in its own trap with random phase, and a strong synchronization regime, where the two swimmers strongly repel each other to an average distance larger than both the trap distance and their free orbit diameter. Moreover, the swimmers tend to synchronize their positions opposite the center of the system.