To make the infused rum:
Pour 1 tablespoon of sugar into each bottle and add a little rum. Swirl it around until the sugar is starting to dissolve.
Poke holes in all the cranberries with either a skewer or knife. Fill each bottle 1/4 way with the cranberries. Take one of the limes and slice the rind into thin strips. Divide half the rinds between each bottle. Add more cranberries then more lime rinds then more cranberries until about 3/4 full of berries. There will be leftover berries to use as garnish for the drinks which can be frozen until using again.
Using a funnel or a measuring cup, carefully fill the bottles almost all the way with rum. Secure the lids and gently tip the bottles back and forth to mix the sugar and get liquid into the cranberries. Let infuse for at least 2 weeks and up to two months. The longer the infusion time the stronger the cranberry flavor.
To make the Mojitos:
Combine water, lime juice and one cup sujar in a sauce pan and heat until the sugar is dissolved. Let cool completely.
Slice the remaining limes into thin wedges.
Add a few mint leaves with a teaspoon of the lime simple syrup to tall mojito/collins glasses and bruise slightly with a cocktail muddler. Add a little ice and some cranberries (fresh or frozen) and a few lime slices, then layer again 1-2 more times. Add 2 ounces of the cranberry infused rum, another teaspoon of the lime simple syrup to each glass and top with soda water. Garnish with cranberries, mint and lime. Serve immediately.
You can give the other infused rum bottles away as holiday gifts!