The 3rd quarter did not end until all free throws related to the intentional foul ended. Once the 2nd free throw ended, the 3rd quarter was officially over.
You would start the 4th quarter as normal, with the home team inbounding the ball and reversing the possession arrow after the throw-in ends (unless of course the home team violates during the throw-in).
If you or your partner had called a technical foul instead of an intentional foul, then you would have started the 4th quarter with a throw-in at the division line, opposite the scorer's table, by the home team. The possession arrow would remain the same after the throw-in ends.
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