How high can a helicopter spot naval gunfire?

Could a helicopter hover above a battleship to improve visual targeting and fall-of-shot correction?

Yes; a Whirlwind-equivalent aircraft has ample ceiling to observe from thousands of feet, though it would still provide visual corrections rather than guided fire.

The Whirlwind benchmark has a service ceiling around 13,000 feet. An observer could therefore hover one or two thousand feet above a battleship to gain a broad view of the target and shell splashes. The aircraft would report visual corrections, with hovering reducing the movement involved in fixed-wing spotting. That elevated observation position would be useful to Warspite and other ships conducting bombardment.