Combine cherries, strawberries, and sugar in a heavy small saucepan. Simmer until almost all liquid evaporates and mixture has jam-like appearance, stirring frequently, about 15 minutes. (As it thickens to this point, you will see the bottom of the saucepan more and more.)

Remove the pan from the heat and stir in the lemon juice. Transfer to a bowl and allow to cool completely.

Preheat the oven to 350 degrees.

Separate the egg yolk from the egg white.

Using food processor with steel knife inserted, process butter, sugar, egg yolk, and almond extract until the mixture is smooth, stopping to scrape down the sides of the processor when needed.

Add the flour and salt in an even layer over the butter mixture and use 4 or 5 on/off turns to mix just until the dough is combined. Do not overprocess or allow the dough to form a ball in the food processor.

Transfer the dough to an 8 X 8 baking dish (preferably glass) and pat down into the bottom of the pan to create an even layer. Whisk the egg white in a small bowl until foamy. Brush the top of the dough with the egg white. Bake crust until the top is golden brown, about 30 minutes.

Cool the baked dough completely.

Spread the cherry-berry jam mixture over the shortbread crust.

Sprinkle the top with the sliced almonds and coconut flakes, gently pressing them into the jam if needed.

Cut bars into 16 squares.