LONDON—U.S. liquefied natural gas (LNG) exporters are emerging as big winners of Europe’s supply crisis as they export record volumes to the European Union for the third consecutive month at prices that have rallied since Russia’s invasion of Ukraine. European gas prices have hit all-time highs just as exporters of LNG in the United States completed projects that had been under development for years to deliver abundant shale gas supplies to international markets. Major U.S. developers like Cheniere Energy Inc, the largest U.S. exporter, are among the top beneficiaries after having signed numerous long-term deals to sell LNG in recent months, traders said. Commodities traders such as Trafigura and Gunvor as well as some Japanese trading houses that have positions in the U.S. liquefaction terminals are also seen as major winners, after having diverted cargoes initially meant for other regions to higher-paying European markets. Russia is a major world oil …