Lightly butter the face of a candy thermometer and set aside.
Put the sugar, cream, chocolate, corn syrup, and salt in a large (4-quart) heavy-duty saucepan and stir with a spoon or heatproof spatula until the ingredients are moistened and combined. Stirring gently and constantly, bring the mixture to a boil over medium heat, 7 to 12 minutes. Cover the saucepan and let the steam clean the sides of the pan for 2 minutes.
Clip the candy thermometer to the pot, being careful not to let the tip of the thermometer touch the bottom of the pot, or you might get a false reading. Let the mixture boil without stirring until it reaches 236°F to 238°F, 2 to 5 minutes. Take the pan off the heat and add the butter, but do not stir it into the mixture. Set the pan on a rack in a cool part of the kitchen. Don’t disturb the pan in any way until the mixture has cooled to 110°F, 1 to 1-1/2 hours.
Meanwhile, line the bottom and sides of an 8x8-inch baking pan with foil, leaving a 2-inch overhang on two opposite sides of the pan. Butter the foil. Set the pan aside.
Remove the thermometer from the fudge mixture. Using a hand mixer, beat the mixture on high speed until it is a few shades lighter in color and thickens enough that the beaters form trails that briefly expose the bottom of the pan as they pass through, 10 to 20 minutes. After beating the fudge, stir in 2-1/4 cups toasted sweetened coconut flakes. Pour the thickened fudge into the prepared pan, using a rubber spatula to help nudge it out of the pot. You can scrape the bottom of the pot but not the sides; any crystals that stick to the pot stay in the pot. Smooth the top of the fudge with the spatula. Sprinkle 1/4 cup of the coconut over the fudge. Set the pan on a rack and let the fudge cool completely, about 2 hours. The fudge will be slightly soft the day it’s made but will firm up overnight.
Turn the fudge out onto a clean cutting board and peel off the foil. Turn the slab of fudge right side up and cut it into 25 equal pieces.
The fudge will keep for a week to 10 days stored in an airtight container at room temperature.