An Iranian refugee who has been waiting 18 months on Nauru for critical heart surgery has been flown to Taiwan for the life-saving operation after the Australian Border Force acquiesced and allowed her teenage son to travel with her.

Fatemeh, 55, has been living in Nauru’s regional processing centre at “high and imminent risk of … heart attack or sudden death”, according to doctors. Border Force had approved her medical transfer overseas, but said she could not take her son with her.

Fatemeh refused to leave her son alone and unsupervised on the island. He has suffered from acute mental health issues on Nauru, where unaccompanied minor refugees have faced significant violence.

“Death and separation from my son is the same for me,” Fatemeh told Guardian Australia. “I would not go anywhere without him. All we have is each other.”

Fatemeh and her son, who is now 17, were flown by a chartered jet to Taipei on Friday at Australian government expense. They were the only passengers aside from Australian government-contracted case management and security staff. She will be admitted to Taiwan Adventist Hospital for heart surgery, according to documents seen by the Guardian, while her son will receive psychological care. It is unclear how long they will stay in Taiwan.

Fatemeh fled Iran in 2013 following a violent family breakdown that forced her to abandon her job and possessions, and leave the country with her son, then aged 13. They have been held on Nauru since August 2013. They have been recognised as refugees, but still live in a tent inside the regional processing centre.

She has nightmares of being killed on a regular basis, as well as fears for the safety and future life of her son Prof Maria Fiatarone Singh

The Guardian, which first reported on Fatemeh’s case in January, has chosen not to publish her surname or the name of her son for privacy and safety reasons.

“Her health status over the past almost four years since her detention began has been noted to have deteriorated significantly,” Prof Maria Fiatarone Singh wrote in a recent medical assessment, obtained by the Guardian.

“Her psychological distress has also increased markedly over time, in concert with the distress and poor condition of her son, who has become depressed, withdrawn, hostile and has twice displayed suicidal gestures.”

Singh’s report said Fatemeh displayed no history of mental illness before seeking asylum and being placed in detention.

“It is clear from the extensive mental health evaluations that she has had, that the psychological pain and distress she feels revolves specifically around the wellbeing and safety of her son … and the despair over the conditions they find themselves in,” Singh wrote.

“She has nightmares of being killed on a regular basis, as well as fears for the safety and future life of her son.

“Her son has never lived apart from his mother and she has legitimate reason to feel that without her to protect him, he may suffer at the hands of others on Nauru or may self-harm if he is left by himself.”

Officials on Nauru confirmed that Border Force had received at least five requests “for medical movement” from doctors for Fatemeh: in September 2016 (twice), November 2016 and January 2017 (twice).

The ABF told her last year, “in line with current policy and as previously explained, your son will need to remain in Nauru while you are temporarily transferred”.

I feel I have been heard. Now I have renewed energy to think about life alongside my only hope, my son Fatemeh

Fatemeh told the Guardian that four years in detention, coupled with seriously deteriorating health, had eroded her belief in her ability to survive.

“When I lived in Iran, despite the terrible difficulties of surviving there, my sense of inner power still enabled me to confront those difficulties ... I felt able to ... stand up for my basic rights,” she said. “But the torture of life in Nauru has eroded that inner power. However, my son’s anxious and sorrowful eyes forced me to say ‘no’ to a slow inner death.”

Fatemeh said having her story heard and acted upon had restored her confidence.

“I feel I have been heard. Now I have renewed energy to think about life alongside my only hope, my son,” she said. “I truly hope that my story … to heal my wounds will inspire all women who feel silenced, who can be encouraged to speak out for their rights, to strive for happiness, for hope and for health.”

The Border Force, which has ultimate authority over Australia’s offshore processing regime, has begun using Taiwan for medical treatment not available on Nauru. Several refugees and asylum seekers have been flown there for treatment.

The policy avoids bringing seriously unwell refugees and asylum seekers to Australia, where they often win court injunctions preventing their return to Nauru. Taiwan is not a member of the UN general assembly, so cannot be a party to the refugee convention. Refugees cannot claim protection there under the convention.

Nauru is one of the few countries that recognises Taiwan’s independence and has formal diplomatic relations with the island. Taiwan, officially the Republic of China, but claimed by the People’s Republic, has a long and controversial connection with Nauru.

Nauru has flitted back and forth between having formal relations with Beijing and with Taipei, choosing one and then the other. Beijing refuses to maintain relations with countries that recognise Taiwan’s independence.

Nauru largely depends on aid from other countries for its economic survival. US diplomatic cables leaked to Wikileaks revealed Taiwan was paying Nauruan government ministers a secret $5,000 monthly stipend in exchange for continuing relations. Other MPs received $2,500 a month. The money was described as “project funding that requires minimal accounting”.

Australia pushed Nauru to sever ties with Taiwan and recommence relations with China, but that was resisted.

The Australian government has consistently declined to comment on Fatemeh’s case.

“Healthcare in Nauru is the responsibility of the government [of] Nauru,” it said in a statement. “Decisions about medical transfers are made on a case-by-case basis according to clinical need, in consultation with the contracted health services provider and the government of Nauru.”