Trim the stems from the dried chiles. Tear chiles into pieces and drop (along with seeds) into a medium saucepan. Stir in the sugars, water, and lemon juice, and bring the mixture to a boil over medium heat. Boil, stirring regularly, until the mixture has reduced to 2 cups / 475 ml, roughly 20 - 30 minutes.
In the meantime, puree the blackberries. I use a hand blender in a small bowl, but a standard blender is also an option. Force the berries through a fine-mesh strainer, and discard any seeds. Set the berry puree aside.
Once the chile mixture has reduced, remove from heat, and (carefully) puree it with a hand blender until smooth. Strain through a sieve into a heat-proof bowl. Press on the remaining solids in the strainer to squeeze out any syrup, and discard the remaining solids.
Whisk the berries into the chile syrup and set aside to cool. Place in a jar, or smaller jars, and refrigerate.