Make the lime simple syrup: In a medium bowl, combine the hot water and sugar and stir until dissolved. Add the lime zest and set aside to cool. Strain through a fine-mesh strainer and discard the lime zest. Refrigerate until ready to use.
Fill a cocktail shaker with ice cubes and add the dark rum, Jamaican rum, orange liqueur, falernum, lime juice, grapefruit juice, lime simple syrup, Pernod and Angostura bitters. Cover and shake well, then strain into a Collins glass. Pack the glass with crushed ice, top with the apricot brandy and serve.