In a small, heavy saucepan, combine the sugar, water and cream of tartar. Heat over medium heat, stirring occasionally, until sugar has dissolved. Increase heat to a boil. Do not stir anymore.
Boil, washing down sides of pan with a pastry brush dipped in cold water from time to time to prevent the sugar from crystallizing, until a candy thermometer registers 240 degrees, about 5 minutes. Remove the sugar syrup from the heat when the temperature reaches 240 degrees.
Meanwhile, whisk the egg whites on medium speed until soft peaks form, about 2 1/2 minutes.
Pour the syrup in a steady stream down the side (to avoid splattering) of the bowl containing the egg white mixture, with the mixer on medium-low speed. Beat frosting on medium speed until cool, 5 to 10 minutes. The frosting should be thick and shiny.
To assemble the cake, place one of the cooled cake layers on plate. You may need to trim the top of the cake to ensure you have a flat surface. Spread the top with half the fruit filling.
Top with the second layer. Spread the remaining fruit filling over the top of the cake only. Ice the sides of the cake with the reserved boiled icing.