The elaborate hi-tech sting involved using apps to clone the phone numbers so as to make calls and texts appear genuine, so duping unsuspecting targets.
It is understood the fraudsters were somehow even able to recount in detail recent transactions where the victim had used her card to her over the phone, which helped persuade her the call was genuine.
Fraud cops are now warning others to be on their guard in an effort to thwart the fraudsters from striking again.
Chief Inspector Arron Clinkscales said: “These fraudsters are extremely convincing and use sophisticated apps which make the call appear to be from a bank or even police, mimicking their phone numbers.”
Fraudsters called the 26-year-old, from Armadale, convincing her that they were from her bank and persuading her and her husband to transfer almost £40,000 into bogus accounts. The Evening News understands the couple had saved the money as a deposit on a new home.
“They ask that you transfer money or remove it from your account however no bank or police officer would ever make such a phone call or request that anyone do this,” warned Chief Insp Clinkscales.
Police issued a step-by-step guide of what a customer should do if they fear being targeted by such a scam.
“If you receive such a call, take details and hang up before calling the bank from another phone,” said Chief Insp Clinkscales. In doing so, customers should dial a number obtained from the phone book or other official source such as letters or statements previously received.
“Staff at the bank will be able to provide you with advice and confirm that your accounts are secure,” he added.
Officers are now trying to pick up any trail left by the con artists by examining calls made and bank accountsgiven.
“Police are working hard to identify these individuals who are preying on members of our communities,” said Chief Insp Clinkscales.
“I would urge everyone to make sure that all friends, relatives and neighbours are aware of our advice and that they do not feel scared or intimidated in the event they receive such a call or email.”
More information on how to protect against scams can be found on the Police Scotland website, while banks also issue guidance.
“Simple measures can be taken, like email filters and [using] the Telephone Preference Service,” said Chief Insp Clinkscales.
The Personal Safety section of Police Scotland’s website gives advice to anyone worried they may have been the victim of this type of fraud.
In May, a new partnership providing an immediate police response to bank branches reporting scams was hailed for preventing £500,000 of fraud.
A Royal Bank of Scotland spokesman said: “We sympathise with anyone who has fallen victim to a scam, and know that this is a very distressing experience.
“We would never ask a customer to move money to another account to keep it safe from scams or fraud, and customers should never make a payment or divulge full security credentials at the request of someone over the phone purporting to be from their bank.
“If a customer receives such a request, they should decline this and report it to their bank immediately.”Anyone with information that can assist officers with their inquiries into phone fraud is asked to contact police via 101 or anonymously via Crimestoppers on 0800 555 111.