Add the applejack brandy, apple cider, Simple Syrup and lemon juice to a cocktail shaker with ice. Shake vigorously and strain into 4 chilled glasses. Float an apple slice on top of each to garnish.
Combine the sugar and 1 cup water in a small saucepan and bring to a boil. Cook, stirring, until the sugar dissolves. Remove from the heat and let cool completely. Keep covered in the refrigerator up to 1 month.
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