The discovery of Mr Tran had narrowed the rugged area being looking at by searchers in helicopters, Ms Vicary said earlier.
Ms Hockridge is survived by her partner Ms McBeath-Rley, two daughters and grandchild.
As the search continues for Claire Hockridge in Central Australia, still missing two weeks after embarking on a bush trek with two companions, NT police have said they are concerned she may have run out of water.
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Ms Hockridge was one of three people who had found themselves lost in the Outback after their 4WD became bogged in the dry sand bed of the Finke River on November 19.
Hockridge, her partner Tamra McBeath-Riley, 52, and their companion Phu Tran, 40, were in an SUV that became bogged in a dry riverbed during an afternoon sightseeing drive on November 19.
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McBeath-Riley told public broadcaster ABC that the trio - accompanied by their blue Staffordshire terrier Raya - had survived by drinking pre-mixed vodka drinks and water from a hole dug for cattle, eating biscuits and sheltering in a hole dug under her vehicle. They spotted Ms McBeath-Riley about 1.5km (0.9 miles) away from the vehicle area after a local resident reported seeing tyre tracks.
Police will prepare a report for the coroner.
Tran was found on Tuesday by rancher Ted Fogarty.
Mr Tran told Mr Fogarty he had left Ms Hockridge behind to look for help.
Mr Tran was found by a pastoralist who was conducting a bore check at the Palmer Valley station south of Alice Springs. The couple was living in Alice Springs and had been showing local landmarks to Tran, who was visiting from the south coast city of Adelaide at the time, according to the Associated Press.
"Even though Claire has died in bad circumstances, we are glad that Tamra and Phu have been found alive and well, and we are extremely grateful to everyone who was involved in that", she said.
Temperatures reached about 40C in the area while the group was missing.