The closer location would have received the signal 16,000 years earlier than us here on Earth. They would still say that it happened 10,000 years before they observed it, but they would still say it happened in year 24,000 BC.
> ... but they would still say it happened in year 24,000 BC.
I can't imagine that they would say that!
I'm sure that you mean the equivalent of 24,000 BC in our reference frame, after Lorentz transformation. Not that they would likely even know about us, or manage the transformation.
Assuming these people 10000 lightyears away from the black hole are also on a planet, their reference frame is almost the same as ours - the relative speed of different planets is very small compared to the speed of light. So they'll agree on when 24000BC is.
