Casey Adams, from from Hill of Beath, died after a "very hard fight" against autoimmune hepatitis, which is thought to affect just 10,000 people in the UK.
She was unable to get the transplant on the NHS because of complications she had suffered after a previous transplant in 2016. Her family needed around £200,000 to pay for the transplant privately.
However, she died after her condition worsened in March and spent her last few weeks in hospital.
The illness causes liver inflammation that occurs when the body's immune system turns against liver cells. It is not clear what causes it, although genetic and environmental factors are thought to contribute.
Ms Adams’s family – her mother, Louise and sisters Caitlyn and Laila - wrote on a Gofundme page set up to help to pay for her treatment: “With the heaviest of broken hearts this update is the one we didn’t want to write. After a very hard fight, yesterday, Friday the 27th of May surrounded by all her family and friends, Casey grew her wings and left us all for heaven.
"As a family we would like to thank you all, from the bottom of our hearts, for the support you have shown in what is the most difficult time of our lives. We want you all to know that your support whether it be donations, shares or words of comfort has really meant the world to us.
"We would now appreciate some privacy to try and begin to process and come to terms with our huge loss.”
The funding page had raised £14,776 since it was set up by Ms Adams’ family in April.
Ms Adams, who had been treated at Edinburgh Royal Infirmary in recent weeks, was diagnosed aged 15 after a holiday to Tenerife in October 2015. Her mother has previously said that she had suffered symptoms for some years before that, but had not been diagnosed.
NHS Blood and Transplant national guidance states that re-transplants need “special consideration dependent on the circumstances that gave rise to the need for re-transplant”.