To obtain the Lost & Found: Wedding Ring quest in Xenoblade Chronicles 3 Future Redeemed, interact with the Request Board in the Command Center of Colony 9. For this quest, you’ll need to find a wedding ring that was lost in Colony 9. You can find this ring in the southeastern corner of the Ruined Town Square.
Once you pick it up, the quest will complete! As a reward, you’ll receive 770 EXP and 2120 Gold.