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Well, I'll give this a try. Provided you are talking about NFHS basketball, or at least a game being played in North America I would suggest this:
The shot by A1 is counted, give them 3. This is irrelevant to what B1 did. Since B1 left the court unauthorized you could indeed assess a T foul (it doesn't matter if he left before or after the basket scored). Thus team A would shoot two T's (etc.). This is by the book
Depending upon the age/level of players and the venue (HS, travel, rec),a ref may want to decide whether he saw B1 "leave the court" For example, if it was a young rec player, or middle school, or any other especially clueless individual, and he quickly stepped back on the court after his error, I would probably let it go. Team B would be inbounding the ball after the hoop and all focus would be on that. Of course, then you may have the after-effect of a B player running on the court seeing only 4 players, and the mess continues...
One thing for sure; Waving off A1's basket and giving the ball back to team A is a very unique way to administer this play. Perhaps it's time for a rules review.
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