Hello, I'm Quinn and here to help!
Yes, in this case, it's better to request a refund, whether you purchased it from Xbox or the Microsoft store, please follow the instructions here to process your refund.
Once refunded, you can either switch your Microsoft account region to your friend's region to buy it, or have your friend buy it directly. Feel free to let me know if you have any questions, I'd be glad to help you further.