International law on state succession developed primarily in the context of decolonisation and the creation of new states after the Second World War. The Vienna Convention on Succession of States in Respect of Treaties addresses treaty obligations but explicitly does not address broader questions of state responsibility. The International Law Commission has done work on succession and state responsibility but has not produced binding rules that would resolve the reparations question in the claimants’ favour.
The most relevant principle is that state responsibility for internationally wrongful acts does not automatically transfer to successor states, particularly where the original acts were lawful under the international law of the time. Since slavery was not internationally prohibited during the period in question, and was indeed explicitly permitted by treaty in many cases, the application of state succession doctrine to a reparations claim is legally uncertain at best.