Add the frozen fruit to a preserving pan with the lime rind and juice. Cover and cook gently for 10 minutes, stirring from time to time, until the juices begin to run.
Roughly chop the fruit while still in the preserving pan, using a knife and fork, if the pieces are very large. Pour in the sugar and heat gently, stirring from time to time, until dissolved. Bring to the boil, and boil rapidly until setting point is reached (10–15 minutes). Skim with a draining spoon or stir in butter if needed.
Leave to cool for 10 minutes so that the fruit doesn't rise in the jars, then ladle into warm, dry jars, filling to the very top and pressing any larger pieces of fruit below the jam. Cover with screw-top lids, or with waxed discs and cellophane tops secured with elastic bands. Label and leave to cool.