Final answer:
The Kurile Island chain is the last archipelago on Earth to be discovered that Russia owns. Japan has offered cash for their return, but the issue is still unsettled. Historical context includes Japan's post-WWII condition and Russia's historical expansion.
Step-by-step explanation:
The archipelago in question that Russia owns and was the last to be discovered on Earth is the Kurile Island chain. The dispute over these islands remains unresolved despite Japan's offer of a substantial amount of money for their return. Control over the Kurile Islands continues under Russian authority.
Furthermore, the ESRI GEO Inquiry into Russian Expansion to the Sea can provide insights into how Russia acquired territories and expanded to become the world's largest country between 1553 and 1914. These historical acquisitions include the Kurile Islands, highlighting Russia's longstanding strategy of territorial expansion.