Combine the vodka, lime juice and pomegranate simple syrup in a cocktail shaker filled with ice. Shake until very cold; about 10 times.
Strain into a highball glass filled with fresh ice.
Top with the chilled ginger beer stir, and garnish with a lime wedge.
Notes
Pomegranate syrup is half pomegranate juice and half sugar heated until the sugar dissolves and then refrigerated.I only had some small bottles of pomegranate/cranberry juice so I used them...worked fine!