Whisk together the apricot preserves and 3 tablespoons water in a small microwave-safe bowl; stir in the dried apricots. Cover the bowl tightly with plastic wrap; cut a small slit in the center of the wrap with the tip of a paring knife to vent excess steam. Microwave on high for 2 minutes. Carefully remove the plastic wrap (be careful to avoid the hot steam) and let the apricots come to room temperature, stirring occasionally, about 20 minutes.
Put 1 teaspoon ricotta in each phyllo shell. Gently press 1 apricot into each shell, slightly to the side, and place 1 raspberry next to it. Drizzle a little of the sauce the apricots cooked in over the top. Repeat with the remaining ingredients and serve.
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