That's physically impossible. You can't observe something that's beyond your "light cone", as any galaxy "moving" (it's not really moving, it's the space that's getting expanding) faster than light would be. What you're referring to is the fact that we can confidently predict that galaxies at the edge of the observable universe, which we currently see moving away from us really fast, but as they were in the distant past due to their light taking billions of years to arrive at us, are currently, if we could actually see them where they are right now (again: we can't), "moving" faster than light away from us.

Once a galaxy has moved beyond or "light cone", it's lost forever: you won't see it again even if you try moving towards it at light speed for all eternity.