Yes, that’s my point. For an outside observer, it will look like the object stops moving. We are talking about three different phenomena:
1: The astronaut falling into the black hole experience time as normal.
2: The information the observer receives make it look like the astronaut eventually stop moving at all.
3: The astronaut crosses the event horizon, even if no information of this reaches an outside observer. Despite the lack of information, it still happens. For the astronaut it happens at normal speed. But how long does it take outside the black hole’s gravity before the astronaut has crossed over? It probably depends on the mass of the hole, so it is impossible to give any exact number, but does it take weeks, months, years or millennia. One can’t see when it happens, but I assume scientists have made some calculations.
The concept of a magical telephone, or a videophone, works good. In science fiction it’s called an ansible I think. But let’s adjust it to the different time experiences. If a group of astronauts are travelling so close to the speed of light that they are experiencing time just half as fast as someone on earth, having a conversation with them will feel like they are talking and moving with just 50% of your own speed. The astronauts on the other hand, will see you talk and move twice as fast as them.
If we use the same videophone when we’re talking with the astronaut about to cross the event horizon, how much slower will he talk and move before he crosses over?
I hope that makes the question clearer.