Authorities in Papua New Guinea, where Beckenridge worked for several years as a helicopter pilot, say a man entered the country on a cruise ship in February using one of Beckenridge's known aliases - that of 61-year-old Australian passport holder John Locke.
An official with the Immigration and Citizenship Service Authority said a Mr Locke arrived at the port of Alotau in Milne Bay Province on a ship from Brisbane on February 17.
He had been due to exit Papua New Guinea by April 19 but there was no record of him having done so. He is viewed as an overstayer and authorities will investigate further.
Beckenridge, a 64-year-old born in Sweden, worked for an aviation firm based in Goroka, capital of the Eastern Highlands province in Papua New Guinea before he quit last September.
He abducted stepson Mike Zhao-Beckenridge, 11, from James Hargest College's junior school in Invercargill on March 13 after losing a custody battle.
His car was recovered from the sea beneath cliffs at Curio Bay in Southland in May. Police have been unable to confirm whether the pair were in it when it hit the water. Their bodies have not been found.
Some friends and neighbours of Beckenridge believe he faked the deaths and fled New Zealand, possibly to Papua New Guinea.
Police are treating it as a missing persons case rather than a murder-suicide. They have live border alerts and are working with Interpol, the intergovernmental police organisation with branches in most countries around the world.
Beckenridge, who has lived in Australia and once worked as a pilot in Afghanistan before one of his colleagues was shot down and killed, has several known aliases.
As well as John Locke, they include John Robert Lundh, Knut Goran Roland Lundh, and John Bradford.
The Immigration and Citizenship Service Authority official said they had not been approached by police from New Zealand or Papua New Guinea, or Interpol about the Beckenridge case.
However, Southland area commander Inspector Joel Lamb said police know the movements of Beckenridge and his known aliases until the time his dark-blue Volkswagen Touareg went into the sea.
"Our staff have continued to work with the Wellington Interpol Office since Mike and John went missing," Mr Lamb said.
"This work includes the liaison with overseas agencies, however the details of the specific agencies and interactions remain part of the investigation and police are unable to comment further.
"Border alerts also remain in place for all known passports held by Mike and John, and to date, these have not been triggered. This, accompanied with the information currently available, suggests that Mike and John have not left the Catlins area."
Mike Zhao-Beckenridge' mother declined to comment.
Beckenridge, who was living in an upmarket Queenstown estate before disappearing, was well-known in Papua New Guinea flying circles.
Pilots recall an experienced, talented and popular commercial pilot.
Pacific Helicopters PNG chief executive Mal Smith, who has been interviewed by police, said he knew Beckenridge had been having "problems getting access to his kid but we didn't know it was to that extreme". He was unaware of Beckenridge's multiple identities.
Aviation expert Peter Clark has said it would be "improbable but not impossible" to flee New Zealand by helicopter.
It would likely require a "fairly capable machine", extra fuel tanks, and a stopover, likely at Norfolk Island.
Norfolk Island immigration officials refused to say this week whether they had any records of Beckenridge, or any of his aliases, having travelled through the remote Pacific island this year, citing the Australian Privacy Act 1988.
Beckenridge was not a registered pilot with New Zealand's Civil Aviation Authority (CAA). The civil aviation authorities of Australia and Papua New Guinea both refused to release pilot licence information, citing privacy legislation.
Criminologist Greg Newbold has said other people have escaped New Zealand undetected. He believed it was possible for someone as resourceful and clever as Beckenridge to do so. The most likely method of leaving the country was by boat, he believed.
Southland's harbourmaster's office, which monitors all the ports and harbours in the region, has had no reports of missing vessels or irregular activity since March 13.
Police have been receiving tipoffs from the public that suggest the pair might be hiding out in New Zealand. However, every sighting has been ruled out after checks.
Customs, which controls New Zealand's borders, has previously refused to comment on the Beckenridge case, referring enquiries to police.
TIMELINE
March 13: John Beckenridge, 64, takes stepson Mike Zhao-Beckenridge, 11, from Invercargill school, in breach of parenting order
March 18: Police seek help to find the pair, thought to be travelling in a dark-blue Volkswagen Touareg
March 21: Confirmed sighting of the pair in bush in the Slope Point area in the Catlins
March 22: Items of interest found in Curio Bay area
March 23: Police divers join search at Blue Cod Bay, but conditions too rough
March 24: Police find vehicle wreckage in sea at Blue Cod Bay; "grave fears" for Mike
March 25: Wreckage confirmed as Volkswagen Touareg
March 30: Police divers confirm vehicle is Beckenridge's
April 8: Detective Sergeant Mark McCloy says "all the evidence" points to the pair being inside Mr Beckenridge's vehicle when it plunged off a cliff
April 10: Police say Beckenridge took Mike camping before the vehicle went off the cliff
April 23: Rough seas continue to prevent recovery of the vehicle
May 8: Divers and helicopter recover vehicle which is taken by boat to Bluff
May 18: Police forensic examinations find "no signs of human remains" in the car
