Finely grate the lime peel, squeeze the juice.
Remove the peel from the ginger and grate finely.
Wash apricots, cut in half, remove seeds and cut into 1 cm cubes.
Put the lime zest and juice, ginger and apricots into a high saucepan together with the preserving sugar and stir. Leave to infuse for at least 2- 3 hours.
Lightly puree the mixture with a hand blender, bring to a boil while stirring, and cook for 4 minutes until bubbly, skimming a few times.
While boiling hot, pour the jam into sterilized twist-off jars to just below the rim and seal tightly.
Place jars upside down on a kitchen towel for 10 minutes, then turn to the other side and let cool completely.