Cut pitted quince and apples into small cubes and put them into a saucepan.
Add freshly squeezed lime juice and stir it.
Add 200 g of sugar and cinnamon sticks, stir and heat slowly over low heat, stirring occasionally, until the sugar has dissolved.
Now bring the fruit mixture to a boil, put the lid on the saucepan and steam the fruits for about 10 minutes or longer until the quince and apple pieces are soft.
Take the saucepan off the heat, remove the cinnamon sticks briefly and puree the fruits with a hand blender.
Mix the remaining 180 g sugar with apple pectin, add it to the fruit mixture and blend.
Put cinnamon sticks back into the fruit mixture and bring to a boil while stirring.
Cook the quince apple mixture until bubbly, 3 - 4 minutes.
Take the fruit mixture off the heat, add rum and stir briefly.
Immediately fill the hot quince and apple jam into sterilized preserving jars up to the rim, removing the cinnamon sticks, seal the jars, put them on the lids for about 15 minutes, then turn them and let them cool.