Not clear (to me) how you anchor rope to the galaxies.
This is because galaxies are gas-like more than they are solid gravitationally bound objects, right? I remember that you mentioned that. Otherwise my guess is that you could have “buoys” in orbit around the central supermassive black hole or at Lagrange points if they exist, to which the rope is attached and then merged into a single rope, which goes to a similar setup in the other galaxy.
This is because galaxies are gas-like more than they are solid gravitationally bound objects, right? I remember that you mentioned that. Otherwise my guess is that you could have “buoys” in orbit around the central supermassive black hole or at Lagrange points if they exist, to which the rope is attached and then merged into a single rope, which goes to a similar setup in the other galaxy.