If by "debts and obligations" you mean nukes. That makes total sense.

They got the seat because they said they did, and no one challenged it:

Boris Yeltsin, the Russian President, informed the United Nations Secretary-General that the membership of the Soviet Union in the Security Council and all other UN organs would be continued by the Russian Federation with the support of the 11 member countries of the Commonwealth of Independent States.

https://en.wikipedia.org/wiki/Dissolution_of_the_Soviet_Union

The UN could kick them off the Security Council if they want. They are not the same country and they are not contributing to world security. This their membership on the Security Council is tenuous.

Russia is breaking current rules that outline which wars are legal and which are not. Wars of aggression are illegal. Even Putin agrees with me. Here's Putin's opinion on war and the UN:

Russian President Vladimir Putin, in a televised conference before a meeting with the US envoy to Iraq, said on 19 December 2003 that "The use of force abroad, according to existing international laws, can only be sanctioned by the United Nations. This is the international law. Everything that is done without the UN Security Council's sanction cannot be recognized as fair or justified."

https://en.wikipedia.org/wiki/Legality_of_the_Iraq_War

Good thing we already have a precedent to change what state the UN recognizes as representative of a country without going through the security council then.