In a small saucepan, bring the pineapple juice, 2 tablespoons maple syrup, the lemon juice and cinnamon stick to a boil. Lower the heat and simmer for 5 minutes; remove from the heat.
Meanwhile, in a medium bowl, beat the cream with the remaining 1 tablespoon maple syrup until soft peaks form.
Divide the pineapple-maple mixture among 4 small teacups or mugs. Discard the cinnamon stick. Add 1/4 cup rum to each cup; top with the maple whipped cream.