Very llightly grease a 20 cm cake tin. Dust with caster sugar, then with flour. Shake out the excess.
Place the eggs and caster sugar in a mixing bowl and whisk with an electric whisk for 5 minutes at top speed. When thick and mousse-like, fold in the sifted flur and salt.
Pour into the prepared tin. Bake in the centre of a moderatly hot oven 190C/375F/Gas 5 for 25 minutes or until golden brown and shrunk from the edges of the tin a little. Run a blunt knife around the inside of the tin and turn out the cake on to a wire rack to cool.
For the filling: Place the apple slices in a pan with the grated rind and juice of a lemon and the jam. Heat slowly. Add the artificial sweetener to taste if required. Cover and cook until the apples are just tender.
When the cake is cool, slice it across with a large knife to make two cakes. Spread the bottom half with the cooled apple filling and cover with the top half of the cake. Sprinkle with icing sugar on top.