Put the frozen berries in a saucepan with the sugar and warm up a little until the fruit is juicy. Mix into puree with a hand blender or in a blender. Strain the puree through a sieve that is not too fine. Mix the berry puree with vodka and lime juice well either in a blender or in another large container.
Fill limes into well rinsed and dry bottles.
Let it steep in the refrigerator for 1 week, shaking well from time to time.