First, the NFHS and NCAA Men's/Women's Rules AP Arrow Rule is identical that includes the wording defining how the AP Arrow is to be initially set. The Rule has never changed since its adoption.
Suprisingly,

, when the NFHS and NCAA Men's/Women's Rules Committees adopted the AP Arrow Rule neither Rules Committee addressed the situation described in the Original Post directly in the Rules, instead, the Committees adopted identical Casebook Play/Approved Ruling with the same Ruling.
I am not going to climb up into the attic but the Ruling for the OP was:
When B1 caught the ball, B1 simultaneously established Player Control/Team Control for Team B and committed a Jump Ball violation. When B1 established Player Control/Team Control the AP was set to Team A's Basket and then Team A received the ball for a Designated Spot Throw-in as a spot nearest to where the violation was committed.
AND THEN, starting with the 1993-94 season the NCAA changed its Ruling in its Approved Ruling. The Ruling said that B1 could not simultaneously establish Player Control/Team Control for Team B and commit a Jump Ball violation, rather B1 can only commit a Jump Ball violation. BUT, the NCAA did something
weird (does that suprise anybody,

) with its Ruling, rather than state that the AP Arrow will be set toward Team B when the ball is placed at the disposal of Team A for its Designated Spot Throw-in for B1's Jump Ball vioation, which the Rule states, the AP Arrow will be set toward Team B's Basket after Team A's throw-in ends.
The following year, the NFHS changed its Casebook Play Ruling to match the NCAA's Ruling except that it stated when the AP Arrow would be set toward Team B's Basket when the ball is placed at the disposal of Team A for its Designated Spot Throw-in for B1's Jump Ball vioation as per Rule.
So endedth the tonight's lesson.
MTD, Sr.
P.S. It was 12:18amEDT when I wrote this post and I was recovering from a long weekend, which will be the subject of another thread, none-the-less, I just now having time to respond to subsequent posts by others.