Two observers fall into separate black holes, then the black holes merge, can they meet again? As far as I understand, both these things take finite time:

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*two black holes merging


in any sensible meaning of the term merge the two black holes do indeed merge in a finite, and very short, time.

So Black Holes Actually Merge! In 1/5th of a Second - How?


*someone falling inside a black hole to reach the singularity


Calculating the lapsed time to fall from the horizon to the singularity of an existing black hole is a standard exercise in GR, and the result is:
$$ \tau \approx 6.57 \frac{M}{M_{Sun}} \mu s $$
That is, for a black hole of 10 solar masses the fall takes 65.7 microseconds!

A Hollow Black Hole
So basically, we have two observers, falling into separate black holes, and then the black holes merge. Since it takes finite time for the observers before they hit the singularity, they could theoretically observe the merger itself (which takes finite time too) from inside. Now if the merger happens so that the two event horizons open up to each other (unite) before the observers would hit their own singularity, theoretically there is a finite period of time when they are reunited into a single common (united) spacetime inside the (merged) black hole. So this is not a violation of escaping the black hole, since none of them need to escape anything. But since they are during the merger inside a common (merged) event horizon, can they meet again?
Question:

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*Two observers fall into separate black holes, then the black holes merge, can they meet again?

 A: I'll try to answer this question based on my intuition about black hole interiors, such as it is, and not any real calculation. A real calculation would be extremely difficult because of the lack of exact solutions describing merging black holes.
Assuming realistic trajectories without enormous acceleration, they probably can't meet. The reason is that your maximum proper time to live once you cross the horizon is comparable to the light crossing time of the black hole (~10 µs per solar mass) while the merging time is probably much larger, depending on how you define it. The two holes that were said to merge in 1/5 of a second had a maximum time to live past the horizon of roughly one millisecond. I don't think you can realistically get from the "leg" to the "hip" region of the interior in that time.
If you treat the star-crossed lovers as classical point particles and allow unlimited acceleration, then I think they can meet, because it's possible to stay arbitrarily close to the horizon after crossing it for an arbitrarily long coordinate (not proper) time. There may be pairs of entry points for which meeting up isn't possible (for example, I think that worldlines that cross a Schwarzschild horizon at precisely antipodal points technically can't meet). But however you want to define "before" and "after" the merger, there should be points that fit your definition for which it is possible.
In the above I assumed that real-world black holes have an unavoidable spacelike singularity like Schwarzschild black holes. Kerr-Newman black holes have interior regions where you can hang out for an arbitrarily long time, and you can definitely meet up in one of those regions. But those regions are not expected to exist in anything but idealized exact vacuum solutions.
