I am not sure if Camponotus ligniperda could live in the nesting box, but it's brilliant for Lasius niger. I have several of those Starter Kits and I keep Lasius niger and Lasius umbratus in them with a lot of success.
Hi and welcome to this forum We have kept C.ligniperda a few times now, Link to a journal without sucess. The Camponotus require loads of space due to their size, so an upright doesn't give the "turn around room" they need. But that set up is fine for your smaller species as you can see on the members journals. Start with something you know will have a better success like the Lasius, and work your way onto others. Some prefer drier nests to others, and some like dry areas and moist areas within the same nests. Messors are another popular starter, but they too like room.
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Camponotus are a very large ant genus, and would need a lot of space which I doubt the starter nest would afford them. This is better for medium sized ants such as Formica, Lasius or Myrmica species as it would give ample space for both queens and workers. Any species from these 3 genera or a similar sized ant should be fine.