Peel the skin off the limes reserving about ½ tsp of grated zest for serving.
In a small saucepan combine 1 and ⅔ cup of coconut cream (refrigerate the remaining ⅓ cup of cream), strips of zest and 7 tbsp of sugar. Bring to a gentle simmer. Cook on a medium low heat stirring occasionally until sugar dissolves and lime infuses the coconut cream, about 5 minutes.
Remove Posset from the heat, stir in ⅓ c lime juice and let it cool to a room temperature. Strain and divide Posset among 4 serving glasses. Chill Posset in a refrigerator until it thickens, about 4 hours or overnight.
Using a hand whisk, beat the remaining ⅓ c of chilled coconut cream with 1 tbsp of sugar and 1 tsp of lime juice until soft peaks. Top each Posset with a sliced strawberry and a few dollops of whipped cream. Sprinkle with grated lime zest.