Accordung to the theory of relativity, there's no such thing as "the same moment" between two distant bodies. When the distance is light milliseconds, we can pretend it does not exist. When it is light-seconds, like between Earth and GEO, it becomes hard to ignore. With many light hours which would separate the telescopes I was talking about, the idea of "the same moment" just becomes nonsensical, even in very approximate household terms.
Such telescopes could, of course, register the same compact body, like an exoplanet, and then their pictures could be put together on one timeline, the planet's, thus synchronized.
Maybe if a pulsar happens to be close (in angular terms) to the object observed, it could help synchronize the pictures. If the pulsar lies in a seriously different direction, it likely would be less helpful: most pulsars have rather short periods, and all pulses are the same.
Such telescopes could, of course, register the same compact body, like an exoplanet, and then their pictures could be put together on one timeline, the planet's, thus synchronized.
Maybe if a pulsar happens to be close (in angular terms) to the object observed, it could help synchronize the pictures. If the pulsar lies in a seriously different direction, it likely would be less helpful: most pulsars have rather short periods, and all pulses are the same.