[Lotto]

Let's say that A1 fouled B1 and B1 shot the FTs inappropriately, after which B2 scores the basket off the rebound.

Since there were no points scored on FT shots and no other "activity" during the FT to cancel, there's no correction to apply. (If B1 had made one or both FTs, then we'd "correct" the error by wiping those points. If there had been a personal foul during the FT, we'd wipe that too.)

The basket counts, since as you rightly point out, it occurs after the FT is completed.

Play resumes at PoI, which is a throw-in for team A at any point along the endline (that is, A can run the endline). This is different than what would have happened if no error had occurred, where B would have been given a throw-in at the spot nearest where the foul occurred.