It applies to both acquiring and recharging the spell. "Against a spell" means any check required by that spell. So if the check is printed on the spell card, it helps with that.
WotR Rulebook p11 wrote:
If a card refers to a check against another card, that refers to any check required by that card, whether it’s a check to defeat, a check to acquire, a check to recharge, or any other check.