Dump the juice from the jar of pickles. Slice the pickles lengthwise and return to the jar. Add the prepared horseradish on top of the pickles in the jar. Combine the water, white vinegar, and sugar in a small pot and bring to a boil. Allow to cool and pour into the jar. Replace the lid and place in refrigerator.
Store in the refrigerator for at least 24 hours. (If you can wait that long!) They will get even better with time.