Is it over
 

Team A is down by 2, with 1 second left. A1 get a shot off from behind the 3 point line. A1 is fouled before returning to the floor. Count the 3 point basket, report the foul, no free throw, A team wins. While walking off the court, coach A gets a T ? :D

Go back. Have A shoot the FT for the shooting foul. Then have B shoot the FTs for the T. Determine whether the game is over or OT is needed.

The hidden question in this thread is after walking away from the foul shots, can you go back and shoot them now?

It wasn't hidden. Yes, you can go back.

Not By The Hair Of My Chinny, Chin, Chin ...
 

2-2-4: The jurisdiction of the officials' is terminated and the final score has been approved when all officials leave the visual confines of the playing area.

A few years ago we had an official from another local board in our state, after leaving the visual confines of the playing area, and entering the officials locker room, come back out onto the floor to correct a bookkeeping mistake in the official scorebook, that led to the "losing" team actually winning the game. It got real ugly. Real, real ugly. Headline above the fold of the sports section of the local newspaper ugly. An article in every sports section of all the state newspapers ugly. Once both of you have left the visual confines of the playing area, don't stop, don't look back, don't answer a knock on the official's locker room door, unless you know for sure that it's a site director offering you some refreshments, or giving you your checks.

Of course our Forum members in the Commonwealth of Massachusetts will do this after observing a bunch of kids shake hands, who don't really want to shake hands. If I'm not mistaken, their jurisdiction is terminated only when the final score has been approved, i.e., their jurisdiction has ended while they are still within the visual confines of the playing area. Plenty of time for some unsporting conduct, correctable errors, or bookkeeping mistakes, to pop up, that can't be charged, changed, fixed, or corrrected, according to NFHS rules. As good, ole Charlie Brown used to say, "Good grief".

The reason we would not normally shoot the free throws is not because they are not merited, it is because they do not affect the outcome of the game, per NFHS 5-6-2 Exception 3: "...No free throw(s) shall be attempted after time has expired for the fourth quarter or any extra period, unless the point(s) would affect the outcome of the game."

But once the coach interjects himself into the OP's situation, the outcome of the game is no longer decided. So we do what we always do which is penalize the fouls in the order they occurred. A1 gets his free throw, then any eligible player(s) from B shall attempt the free throws for the T. If at any point during that process the game again becomes decided (e.g., A1 makes his free throw and B misses the first), then we stop. Otherwise, we shoot them all, and if the game is tied, we go into overtime.

Which brings up the next question. If we go into overtime, and the last foul was the T on A's coach, does OT begin with a jump ball or an AP throw-in? :D

Since teh T was part of the 4th quarter and not part of the OT (yes, I know that technically the OT is an extension of the 4th quarter), start the OT with a jump ball.