Ooh, that's a good one.
I'm going to say that this isn't covered in the rules and rule according to what seems fair to me, as authorized by 2-3.
In losing possession before completing the throw-in, A1 would have had to violate, either a 5-second violation or a throw-in violation to go fetch the ball. So I'm going to penalize A for a violation, awarding B the ball at the OOB spot.
I can see arguing the other way: B2 violated by reaching across the plane to get the ball, and B2's violation occurred before A1 had the chance to violate.
But I think A1 screwed up first, even if it wasn't yet a violation, and that was the occasion for B2 violating. I'm disinclined to reward A with another throw in.
Did you construct this, or find it somewhere? Or did it really happen?