Injured Player Returning With No Time Off Clock

[FeetBallRef]

As time runs out in the 2nd quarter, A1 is fouled in the act of shooting & has to be replaced & A6 shoots A1's foul shots. By rule, it appears that A1 can't start the 3rd quarter even though 10 min. have passed. Is there any provision in the rules that would allow him to return before time has run off the clock?? Should officials be aware of this because there probably isn't a score keeper who would catch it??