The man, under instructions from the scammer, then deposited nearly £3,000 with cryptocurrency seller Coinbase.
Despite the family’s attempts, they were unable to withdraw the funds.
A Coinbase spokesperson said it encouraged all its customers to “thoroughly research any investment opportunity they come across online”.
“We also share tips with our users on how to spot investment scams,” they said.
The National Fraud Intelligence Bureau, Action Fraud and the Financial Conduct Authority have been alerted to the scam.
The family member added: “I’ve been told that it is very unlikely that we will be able to get the money back.
“It’s a shock to the system, really, as that was a large chunk of their life savings just gone.
“I don’t have words for these scammers, if they were any kind of decent human being if they would have compassion.”