Select the raspberries, wash and drain. Then mash them with a wooden spoon. Stir in rum. Peel and slice the limes. Add jam sugar to the cold fruit mass and stir in evenly for 2 minutes.
Pour the jam into the prepared jars. Carefully dip 2-3 lime slices per jar into the jam using a spoon handle. Consume the jam within 2 days or freeze it immediately and consume within approx. 4 months.