The 2015 deal, in which fashion, food and leisure operator Cheil Industries took over construction company Samsung C&T for $8.0 billion, featured in the sprawling corruption scandal that brought down ousted president Park Geun-hye.
It went through after the National Pension Service (NPS) -- C&T's biggest shareholder -- approved it.
Prosecutors accused Lee of seeking government backing for the deal, and at trial he was found guilty of bribery and sentenced to five years in prison, although most of his convictions were later overturned on appeal.
Now US-based Elliott, whose whose 7.12 per cent stake in C&T made it the company's second-largest shareholder, has sent a "notice of arbitration" of an investor-state dispute to the South Korean government, the justice ministry said in a statement.
"In the notice, it claims it suffered no less than $770 million damages from the merger between Samsung C&T and Cheil Industries as a result of the government's 'illegitimate' intervention," the ministry said.
The government -- now led by Park's longstanding opponent Moon Jae-in -- had launched a joint task force to address the issue, it said.
At his trial, prosecutors argued that Moon had been ordered to support the deal by then-president Park, who was subsequently jailed for 24 years for bribery, coercion and abuse of power.
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