1. Line a 9 x 5 x 3-inch loaf pan with nonstick aluminum foil.
2. Pour cognac into 1-cup glass measure. Microwave on high for 1 minute until hot. Stir in apricots. Cover; let sit for 1 hour, stirring occasionally, to absorb liquid.
3. Bring cream just to boiling in a heavy medium-size saucepan over medium heat, about 2 minutes. Remove from heat. Add chocolate and butter, stirring until chocolate is completely melted. Scrape into prepared pan and refrigerate, covered, 1-1/2 hours or until just firm.
4. Line an airtight container with waxed paper. Sift cocoa powder into a small shallow bowl; sift confectioners sugar into a second small shallow bowl. Place coconut in a third small shallow bowl.
5. Holding edges of aluminum foil, lift candy out of pan. Cut chocolate into 24 pieces. Make an indentation in the center of each piece using the handle of a wooden spoon. Press an apricot quarter into each indentation.
6. With hands, quickly shape chocolate into a ball around fruit; mixture will be messy. Refrigerate 10 minutes. Remove and roll again into a smooth ball. Coat a third of the truffles in cocoa powder, a third in confectioners' sugar and a third in coconut. Refrigerate for at least 15 minutes to firm. Can be refrigerated up to 2 weeks or frozen up to 3 months.