Quote by Gio83
Long story short: from the point of view of A, will B ever cross the horizon?
And: given the relation that links the radius of the EH with the mass beyond it, how can a black hole grow (from the point of view of a distant fixed observer) if everything will fall behind the EH only for t→∞ ?

Short story long:
Imagine an observer falls into a black hole. Lets say it takes him 10 seconds to arrive at the EH and 20 seconds to arrive at the singularity as measured by his own clock. As measured by a clock far away from any massive objects, an infinite amount of time will have passed before 10 seconds registers on the infalling observer's clock. In that time the Universe will have expanded and the background temperature of the universe will be near absolute zero degrees Kelvin. Black holes will have evaporated before that 10 seconds passes on the infalling observer's clock and in this analysis the Black hole will be gone before the observer arrives at the EH. The problem with this analysis is that it uses the static solution and ignores the mass of the infalling observer. What actually happens is that the mass of the infalling observer contributes to the total mass of the black hole gravitationally and EH expands and moves outwards to meet the the faller. In this way mass can arrive at and pass through the EH in finite time, even from an external coordinate time point of view.