More than £1m has been recovered for 153 UK victims of fraudulent overseas share-selling operations, known as "boiler rooms".
The FSA offers advice on its own website
The Financial Services Authority (FSA) said it had helped the authorities in Canada retrieve most of the £1.25m that had been sent there.
The investors had been conned by phone calls from crooks who were selling shares in two gold-mining companies.
The FSA said the investors were lucky to get most of their money back.
"This is a rare bit of good news for investors who have been persuaded to hand over money to boiler rooms, as usually the money disappears without a trace," said Jonathan Phelan, head of the FSA's enforcement division.
The boiler rooms had acted illegally by selling, without authorisation, shares in the Rocky Mountain Gold Mining Corporation and the Rocky Mountain Gold Mining Inc.
Unusually, in this case the authorities were able to recover most of the money.
The British Columbia Securities Commission, and the Ontario Securities Commission, were able to freeze the funds before the boiler room operators disappeared. About 90% of the money has been recovered.
People who have bought shares in the two gold-mining companies are advised to contact the FSA, as they may not be aware that they can get their money back.
"Any investor who has not yet been contacted by the FSA or the Ontario Securities Commission should call the FSA's consumer contact centre on 0845 606 1234," the FSA said.
Boiler rooms are defined as share selling operations operating abroad, which are unauthorised by the FSA, and in which the shares sold are "overpriced, restricted for onward sale and have little or no realisable value."