In a medium saucepan, heat the vinegar until it is steaming hot, just about to break into a bubbling boil.
Remove from heat. Place the trimmed and quartered strawberries in a large heatproof bowl and pour the hot vinegar over them; vinegar should cover the berries by at least one inch.
Let stand at room temperature for 18 to 24 hours.
Strain the vinegar into a medium saucepan, leaving the berries behind in the strainer. Don't press them. Discard the berries, and add the sugar to the vinegar in the saucepan.
Bring to rolling boil, stirring to dissolve the sugar. As soon as the sugar is dissolved, about 2 minutes, remove from heat and let the shrub cool to room temperature.
Pour the shrub into a clean, sterilized jar and cover tightly. Store in the refrigerator for up to 3 months.
To enjoy your strawberry shrub, fill a tall glass with crushed ice, or ice cubes. Add about ¼ cup strawberry shrub to the glass.
Pour club soda, or mineral water, or selter water over the ice gently, so that the shrub stays at the bottom. Serve as is, and let each guest stir up their beveraage; or stir each glass to combine the shrub with the water and then serve.
