I did see Can black holes form in a finite amount of time? but it does not seem to discuss how a distant observer would see evolution of collapsing matters that form a black hole. Does it view these matters as disappearing under the horizon, or does it see being radiated back by Hawking radiations, with a distant observer unable to actually see matters falling into the horizon?
Strictly speaking the far away observer never seen the black hole forming, and after a while it will start receiving Hawking radiation, until nothing is left. The evaporation process can be thought as starting slightly outside the horizon (at a Stretched horizon). This is pictured in the image on the left, a Penrose diagram of an evaporating black hole (remember that light travel at $45°$ degrees here)
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