How can information ever get lost at the event horizon of a black hole?

In the drawing, A and B are two entangled particles in Kruskal coordinates, A is falling into the black hole, B is remaining outside.

The lines going through the center are the time coordinates of the far-away observer : t = 0, t = 1, t = 2, limited by the event horizon where t = $\infty$. Until the end of time t, the worldline of B is remaining outside the event horizon, and until the end of time t, the worldline of A is on its travel to the event horizon without ever reaching it.

The question: As A will never reach the event horizon, according to the time coordinates of the far-away observer how could information ever get lost from the point of view of the reference frame of an outside observer? If information is remaining outside the event horizon until the end of time, I do not see how there can be any issue of loss of information in a black hole.

Note: I am aware of the fact that the result is very different from the point of view of the infalling observer A. According to the reference frame of A, A is entangled with B until it crosses the event horizon, and at this moment it is losing suddenly the entanglement.