This certainly looks like a scam. It is better known as 'boiler room' fraud and usually involves the sale or transfer of company shares.
The ways in such scams operate are as follows:
· You are contacted, most commonly cold-called, by a company that offers to buy existing shares off you. You may even have been the victim of a similar scam in the past and they are offering you a lifeline by telling you they can buy these shares off you and return some of the money you have lost. Often they will be linked to the original fraudsters or your details would have been obtained from publically available shareholder lists.
· If you are selling your shares the scam would involve a request for a payment in advance. This could be for various reasons, such as commission, security, insurance, taxes, etc. None of these would ever be required in real life and you should not have to pay any such fees in advance of the sale.
The broker is unlikely to be a real and legitimately registered company. They are also commonly working from professionally looking websites, which have been created very recently. This is because they would have only been created for the purpose of the scam and would not last long before being taken down by the authorities.
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