Replacing the injured free thrower

[griblets]

In my GV game last night, shooter A1 is fouled by B1 and injured, requiring A1 to leave the game. We inform Coach A that the replacement A6 will shoot the free throws. Coach B thinks that Coach B gets to choose A's substitute for the free throws. My partner (with 20-25 years experience NFHS and NCAA) was confused, stating he never heard such a rule. However, I (with 6 years experience from 16 years ago) seem to have some vague memory of a case play or situation where Coach B would get to choose A's substitute for free throws. Is this an NCAA or NBA rule? Is this an old NFHS rule? MTD recently referenced a rule change from 1963, so I'm looking at him! Maybe it's for the case when there is no substitute available? Maybe I'm just as delusional as Coach B?

FWIW, we quickly and correctly allowed Coach A to provide substitute A6 to shoot the free throws. (NFHS Rule 8-2)