In June, Russian President Vladimir Putin took over the LNG project, creating a new legal entity to deal with buyers and shareholders.
MOL signed a 60 percent stake in a subsidiary that is owned by MOL on Tuesday with new operator Sakhalin Energy LLC.
The vessel is carrying LNG from the project under a long-term charter contract with Sakhalin Energy Investment Company Ltd, the former operator, and will continue the same services with the new operator, MOL said.
MOL said it complied with international sanctions and that it continued to consult with various parties, including the Japanese government and project partners, in a likely reference to Western measures against Russian over its invasion of Ukraine.
Sakhalin-2 is one of the world's largest LNG projects, providing about 4 per cent of the global market.