Stir together water, CurrantC™ Black Currant Nectar, 1 1/4 cups Black Currants, 1 cup raspberries, jelly, sugar, and vanilla in a 3-quart saucepan.
Simmer, stirring occasionally, until berries are softened, 6 to 8 minutes. Force mixture through a fine sieve into another saucepan. Discard seeds.
Bring berry sauce to a simmer and vigorously whisk in arrowroot mixture. Simmer, whisking constantly, until thick and glossy, about 2 minutes (do not boil).
Remove from heat and stir in strawberries and remaining blackberries and raspberries.
Transfer pudding to a serving bowl and cover surface with a piece of wax paper to prevent a skin from forming. Chill until cold, at least 2 hours.