Mix the syrup with the water. Wash the mint well. Wash the limes with hot water, rub dry and cut into slices. Let everything steep in the elderflower water for a few hours.
Put all ingredients in a sufficiently large container, ideally with an outlet on the bottom, and let it steep in the refrigerator. The limes and peppermint give off more flavor over time. If it gets too strong, simply dilute the drink with water and elderberry syrup.