Xbox Cross-Gen Edition: Includes a cross-gen version of Call of Duty: Modern Warfare II playable on Xbox Series X and Xbox One. PlayStation 4 Cross-Gen Edition: Includes a cross-gen version of Call of Duty: Modern Warfare II playable on PlayStation 4 and unlocks a free digital upgrade to play on PlayStation 5.

Sorry you will have to buy it again. Games you buy for Xbox can't be used on Playstation and so. They require their on version.