The Australian climber arrived in Kathmandu from Everest base camp on Tuesday and went straight to hospital, Australian Himalayan Foundation chairman Simon Balderstone said in a statement.
"He immediately went to the Nepal International Clinic with the Russian expedition doctor, Andrey Selivanov, who had been looking after him since his rescue," Mr Balderstone said.
"The clinic doctor considered his condition amazing given what he had been through, and at such an astounding height on the mountain."
Mr Hall, 50, was presumed dead on Thursday after becoming disoriented from the effects of cerebral oedema, an acute form of altitude sickness, on his way down from the summit of Everest.
An American mountaineer found him alive the next day and he was rescued by a team of sherpas.
Mr Hall, from the Blue Mountains near Sydney, survived a night exposed on Everest in the “death zone” at a height of 8,700 metres.
He is still suffering traces of pulmonary oedema, fluid on the lungs, as well as frostbitten fingers, one frostbitten toe, a chest infection and the continuing effects of cerebral oedema, or fluid on the brain, Mr Balderstone said.
Mr Balderstone said the chest infection "should clear up soon" with the moist air and lower altitude of Kathmandu, combined with medication.
"Overall he is in great shape and is very grateful for all the support he has received on the mountain, here in Nepal, in Australia, and from friends in many other countries," Mr Balderstone said.
Meanwhile, Mr Balderstone said the foundation was terribly sorry and upset about the death of fellow Australian mountaineer Sue Fear, a friend of Mr Hall's.
Ms Fear, 43, of Sydney, died after falling into a crevasse on
Nepal's Mt Manaslu, the world's eighth highest mountain, on Sunday. She was less than 500 metres from the summit.
"Our deepest sympathies go to her family," he said.
"Sue was the Australian Himalayan Foundation's first honorary member and raised thousands of dollars for the foundation so we could further help the people of the Himalayas,” he said.
The Fred Hollows Foundation has also paid tribute to Ms Fear, who became an official ambassador of the foundation in 2003.
She used her public profile to support sight-saving operations in her beloved Nepal, foundation CEO Brian Doolan said.
"Sue was a beautiful person, a great Australian and an inspiration to The Fred Hollows Foundation and to all those who knew her," Mr Doolan said.
Ethics debated
Ms Fear’s accident and the miraculous survival of Lincoln Hall, follows the recent death of British climber David Sharp, who was left for dead high on Mount Everest, whilst dozens of climbers walked past him to the summit.
Mr Sharp’s death, and the survival of Mr Hall, has re-ignited debate about the ethics of expeditions in the Himalayas.
Duncan Chessell from expedition company DCXP Mountain Journeys says there are many factors to consider in attempting a high-altitude rescue.
“You've got to be in the position to offer assistance and for that not to be something that will kill you as well. Once you've got through that part of it, basically you do what you can, and of course generally you get as many people involved from your team or other teams, into the rescue situation, that can possibly help at any one time,” Mr Chessell said.
Isolation was much of the reason Ms Fear could not be saved on Manaslu.
Her climbing partner Bishnu Gurung was unable to pull her out of the crevasse and a helicopter mission later failed to find her body.
Friend and co-worker Sue Badyari says any attempted rescue in such a remote area is extremely risky.
“Any kind of rescue at high elevation is going to be difficult, but particularly when it's a remote mountain like that as well, where there are few people around,” Ms Badyari said.
Ms Badyari says Lincoln Hall is alive today because of the amount of traffic travelling up and down Mount Everest.
“One of the benefits of course of Everest, if there is a crisis, is that there are more people that can potentially help, and that was of course the really stark difference between the Lincoln Hall and Sue Fear stories,” Ms Badyari said.
But that didn't help David Sharp, who died on Mount Everest after being passed by 40 other climbers.
Mr Chessell says many of those climbers may not have even been aware he was alive.
“There's a lot of other bodies of people who've died there in previous years who are frozen there, and it would be fairly easy to mistake somebody in the dark, who was almost frozen to death, as being perhaps a dead climber. So a lot of them probably walked past oblivious to his being there,” he said.