Step 1Grate enough of the limes with a box grater or microplane to get one-half teaspoon zest. Spread half the zest on a sheet of wax or parchment paper to dry. Reserve the remaining fresh one-fourth teaspoon zest. Juice the limes to get approximately one-fourth cup juice.
Step 2In a small saucepan, dissolve the sugar in one-half cup water and bring to a boil. Reduce heat to a simmer and cook to a syrupy consistency without stirring, about 15 minutes (about 230 degrees). Remove from the heat and cool to room temperature. Stir in the fresh undried lime zest and 1 teaspoon lime juice. Set aside.
Step 3Butter the bottom and sides of an 11-by-8-inch tart pan with a removable bottom. Unfold the puff pastry and roll out creases with a rolling pin. Drape the dough up onto the rolling pin and lift onto the tart pan. Gently ease the dough into the tart pan pressing it onto the bottom and against sides of the pan. Press the dough around the top edges of the pan to cut dough even with the top of the tart pan.
Step 4Brush the bottom and sides of the dough with beaten egg mixed with 1 teaspoon water. Refrigerate 30 minutes. Prick the dough over the bottom and sides with a fork or run a dough docker over the bottom of the tart. (It is unnecessary to use pie weights.)
Step 5Bake 25 to 30 minutes in a 350-degree oven until the pastry is golden brown. If the bottom of the dough puffs too much during baking, gently press it down without breaking the pastry. Remove from the oven and let cool to warm. When the pastry is cool enough to handle, gently loosen the sides of the shell from the pan with a knife, and remove the shell to a serving platter.
Step 6Cut the cherimoyas into quarters. Peel each quarter and cut into one-fourth-inch-thick slices, removing seeds with the tip of the knife as you slice. Brush the slices with the leftover lime juice as you slice them to prevent browning.
Step 7Arrange cherimoya slices on top of the baked puff pastry in an attractive pattern. Brush the fruit generously with the lime syrup. Sprinkle the dried lime peel over the tart. Scatter raspberries over the top, so each serving has a raspberry. Cut into slices and serve.