High-bandwidth internet in orbit is nothing new; the ISS even has a livestream. But that's in low-earth orbit, well below the geostationary satellites that relay the data. My question concerns satellite internet reaching geostationary orbit (GEO) itself. And by internet access, I mean at least enough bandwidth to do a video call.
More specifically, I'm interested in a near-future case where a team of astronauts take a space elevator from the surface of the Earth up to a station at GEO, then board a ship docked there. Assuming wired internet can't propagate along the elevator, will they ever experience a loss of internet connection at any point along this trip? And if so, could this issue be solved by simply having a relay at the station?
I'm relatively sure there shouldn't be a problem, but I'm not familiar enough with how satellite internet works to be positive.