Soak the gelatin sheets in a bowl of ice water until softened, about 15 minutes. Drain, squeeze out as much water as possible, and put the gelatin in a small bowl.
In a large bowl set over a saucepan of simmering water, whisk the sugar with the egg yolks and lemon juice until tripled in volume and very shiny, about 4 minutes. Add the gelatin sheets and beat until dissolved. Remove the bowl from the heat and let the mixture cool completely.
Fold the quark into the egg-yolk mixture. Gradually fold in the whipped cream.
Using a long serrated knife cut the genoise into 2 horizontal layers.
Spread a thin layer of jam on the sugar dough in the pan. Set the bottom layer of genoise on the dough, cut side up. Pour in the mousse and gently tap the pan on the work surface so that the mixture flows down the sides. Set the second genoise layer on top, cut side down, and gently press it. Freeze overnight
Release the sides of the pan and remove the parchment paper. Spread a layer of jam on top of the cake. Transfer to a cake plate, decorate with the fresh berries, and serve.
To serve/cut beautiful slices: dip a smooth, 12-inch knife into very hot water and press straight down through the cake. Clean knife and re-dip into hot water for each slice.