For this recipe the gooseberries should be firm and not too ripe so they don't fall apart when boiled. You can either simply fill them into jars, or process in a boiling water bath for 20 minutes for long-time storage.
Bring the water with the sugar to the boil in a saucepan and stir until till the sugar has dissolved completely. Remove from the hob and let cool.
Fill a large bowl with cold water and place the elderflower umbels in the water with the stems pointing upwards. Move the umbels back and forth a few times to remove any insects. Repeat with a fresh batch of water.
Let the elderflowers drain by shaking them gently but not too much so you don't remove the pollen. Trim as much of the green stems as possible. Place the elderflowers in the cooled syrup and so they are fully immersed. Cover and let sit at a cool place for 24 hours.
The next day line a sieve or a colander with four-fold muslin or cloth and strain the syrup into a jug.
Wash and trim the gooseberries and sort out any blemished ones.
Now you have two choices. Method 1 (preserved this way, they keep several weeks): Bring the syrup to the boil in a large saucepan and add the gooseberries. Cook until slightly softened, 1 to 2 minutes. Place the gooseberries with the syrup in hot sterilised jars and close the jars immediately.
Or, Method 2 (keeps 1 year or longer): Bring the syrup to the boil, place the gooseberries in sterilised jars and add the boiling syrup to cover and close the jars with lids. Process in a boiling water bath for 20 minutes.