Yes, your relative in the UK can get warranty service for the MacBook Air M4 as long as it's within Apple’s global warranty. They can also buy AppleCare at a UK Apple Store, but it’s best to add it when you buy the laptop or within 60 days. Since you’re buying from B&H Photo (an authorized dealer), you can add AppleCare at checkout or register it online, and the coverage will be good no matter where they get the laptop serviced. The warranty should still work for them, even if the receipt is in your name, as long as they have the serial number.