It is normally not possible to pack a fully stacked campfire with stone and firewood into your backpack but if you disasseble it outside and reassemble it in your backpack, thats another story. If you want to take it out of your pack, it will not let you until you disassemble all parts of the whole. If the fireplace is empty you are able to put it out of your inventory againe. For disassebly you need room in you inventory for the parts to see the options for the rightklick menue.
- Legacy ID
-Disassemble fireplace kit which contained firewood and stone.
-Reassemble in your backpack.
-to take it out of your inventory disasseble with enough space for stone and wood.
I was able to verify that with stove and cooking pot too.
Did not try to put cookables in the free space of the cooking pot.