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They found that it had been bought 'very recently' by someone who gave a woman's name - but was using a false identity.
The discovery raises fears of a possible link between Captain Zaharie, 53, and terror groups whose members routinely use untraceable SIM cards. Everyone else who spoke to the pilot on his phone in the hours before the flight took off has already been interviewed.
In a separate development, The Mail on Sunday has learned that investigators are now poised to question Captain Shah's estranged wife in detail.
They have waited two weeks out of respect, but will now begin formally interviewing Faizah Khan following pressure from FBI agents assisting the inquiry.
Although the couple - who have three children - were separated, they had been living under the same roof. A source said: 'Faizah has been spoken to gently by officers but she has not been questioned in detail to establish her husband's behaviour and state of mind in the days leading to the incident.
'This is partly for cultural reasons. It is not considered appropriate in Malaysia to subject people in situations of terrible bereavement to the stress of intensive questioning.' The softly-softly approach has been challenged by the team of FBI agents working with Malaysian police. They have pointed out that she may hold 'vital clues and information' to Zaharie's mental state.
'The whole world is looking for this missing plane and the person who arguably knows most about the state of mind of the man who captained the plane is being left alone,' said a source close to the FBI team.
The source added: 'If we want to eliminate the chief pilot from the inquiry, we must interview her in detail to find out what his state of mind was.'
The mystery caller emerged when Malaysian investigators examined the phone records of both Zaharie and his co-pilot, 27-year-old Fariq Abdul Hamid. Investigators were keen to trace the caller and interview them, although they have stressed that the fact the SIM card was registered to a non-existent ID card does not necessarily indicate a criminal or terrorist connection.
Political activists in Malaysia sometimes use SIM cards bought with bogus identity cards if they fear that their phones may be bugged by the country's authoritarian ruling party.
The Mail on Sunday revealed last week that Zaharie is an avid supporter of opposition leader Anwar Ibrahim, a distant relative, and may have attended a controversial court hearing where Anwar was jailed for five years. It took place only a few hours before the flight. The timing of the call has intensified scrutiny on Zaharie as investigators struggle to establish whether the cockpit crew, a catastrophic accident or hijackers are to blame for Flight MH370's disappearance.
Image 1 of 43: Christchurch man Paul Weeks who is thought to be on Malaysian airlines flight MH370 which is currently missing, presumed crashed. https://www.facebook.com/danica.weeks Sourced from Danica Weeks open Facebook page
Meanwhile FBI experts in the US are continuing to examine the hard drive of a flight simulator seized from Zaharie's home after it emerged that programs he used on it had been deleted. Zaharie used the home flight simulator to practise extreme landings, including on remote Indian Ocean islands such as the US air base in Diego Garcia, investigators have revealed.
The hard drive was flown to the FBI laboratory in Quantico, Virginia, at the end of last week after Malaysian investigators failed to retrieve the deleted files, which they suspect may have been 'buried' in an elaborate process to cover the user's tracks. The delay in handing the computer hard drive to the FBI has proved to be a source of friction between the Malaysian and US investigators, the source close to the FBI said, adding: 'We have the technology to do this work quickly and effectively and they simply don't.'
Malaysia's acting transport minister Hishammuddin Hussein yesterday said investigators are coming under increasing pressure as they are aware that time is running out - the black box voice and data recorder only transmits an electronic signal for about 30 days before its battery runs out.
But he claimed a thorough investigation of the plane's cargo manifest had not shown 'any link to anything that may have contribution to the plane's disappearance'.