In a high powered blender, blend coconut milk, coconut sugar, shredded coconut, lemon juice, and vanilla extract.
Place chopped strawberries in the popsicle mold, dividing them evenly.
Pour coconut milk mixture over the strawberries so it fills up 2/3 of the popsicle mold. You should have some coconut milk mixture left over. Set aside.
Freeze for 30 minutes.
Once partially frozen, push down the popsicle sticks into the middle of the mold until they stick through the frozen layer so they stay in place.
Place blueberries in the mold on top of the coconut milk layer, pushing some down to the middle of the mold
Pour the rest of the coconut milk mixture over the blueberries to the top of the mold.
Freeze the whole thing for at least 4 hours.
When ready to eat, run the mold under warm water to remove the popsicles.