As I understand, Russia will have a right to claim on old Russian empire territories + Alaska. But it won't have any rights in UN. Am I right?
TL;DR: What would happen then? The direct answer is: a legal, administrative, and political disruption.
Modern-day Russia is, indeed, a successor of the dissolved "USSR". Many local laws in the Russia has not been changed since the "Soviet" times. Quite a few international treaties apply since then. Including, but not limited to, the seat in the UNSC.
On the other hand, the Russian Federation is not a successor of the Russian Empire.
After the abdication of Nicholas II on 15 March 1917, there have been five "Russias":
- Provisional Gov't (1917/03/15 – 1917/09/14)
- Russian Republic (1917/09/14 – 1917/11/07)
- Russian Democratic Federative Republic (1917/11/25 – 1918/01/19)
- Russian Soviet Federative Socialist Republic (1918/01/25 – 1922/12/30)
- USSR (1922/12/30 – 1991/12/25)
Transitions 1→2 and 2→3 can't be considered legal successions, so USSR is not a legal successor of the Tsarist Russia, hence the Russian Federation isn't.
This includes renouncing all foreign debts incurred by the Imperial regime:
According to the data presented by the Soviet Government at the 1922 Genoa Conference, the total external national debt of Russia (state and government-guaranteed loans) had amounted by the year 1914 to 6.3 billion golden roubles (at the pre-war exchange rate of the Rouble when it equalled 0.5 USD or 2.16 German RM).
After today's Russian Federation has been established, their government put some effort to pay off the Tsarist debts, with partial success. This thread at Google answers has a lot of useful links on the topic.
As per Alaska, it looks pretty simple:
- Alaska has been sold, check paid;
- There are rumors, mostly in Russian propaganda, containing various claims, none of which seem to be backed with credible evidences.
Hence, claiming the Russian Federation a successor of Tsarist Russia would not let claim Alaska back.
Besides the rumors, Russian "lawyers" recently make many questionable claims:
- The Russian chief prosecutor's office is to examine whether the Soviet Union acted legally when it recognized the Baltic states' independence in 1991 (BBC), therefore challenging an unknown number of USSR's and Russian Federation's legal acts since 1989.
- The "Prosecutor" of the occupied Crimea has stated that abdication of Emperor Nicholas II has no legal force (video, in Russian), therefore challenging the transition 0→1, see above.
Summary. Russian officials, along with the Russian propaganda, can, indeed, make any statements, just like they always do. These statements may or may not be internationally recognized. However, each statement has legal consequences, and these, most certainly, will appear contradictory to each other. Which, in turn, would lead to major disruption of international treaties yet remaining valid.
This question is based on false premises. The original poster's "understanding" is incorrect.
Russia is the successor state to the Soviet Union, which in turn was the successor state to the Russian Empire. The current incarnation of Russia has recognized the independence of Poland, Finland, and the non-Russian former Soviet Socialist Republics.
The current incarnation of Russia has also recognized the so-called independence of a few so-called states that are not recognized by any other countries. These disagreements amount to military occupations of portions of some of Russia's neighbors by Russia.
Russian Federation was not successor to Russian Empire because USSR was not successor to it.
Even IF Russian Federation claim they were successor, only that to get Alaska back is demonstrate that USA violated agreement. USA didn't do so. Agreement was signed. Money was sent (historical documents is not fully clear on whatever money was received and signed for by Russian Empire).