Cystic fibrosis sufferer Kimberly Chard, from Bargoed, Caerphilly county, received a life-saving double lung transplant on Christmas Eve.
The 32-year-old, who is recovering at London's Harefield Hospital, said she is still coming to terms with the family's "selfless gift".
"I will always be grateful for the future they have given me," she said.
The life-threatening genetic disorder damages the lungs and digestive system.
"I'm still trying to take in this selfless gift I was given by my donor and their family and the fact that they still chose to save someone's life so close to Christmas.
"I understand their grief that they're going through, but I hope they're comforted by the lives that they have saved.
"I will always be grateful for the future they have given me and I can't wait to see how I keep progressing day by day."
Ms Chard was told in March last year her condition had deteriorated so much she would die without a double lung transplant.
After months of struggling to breathe and waiting for the phone to ring, the call finally came on 23 December. She had her operation the following day.
"I'm just so blown away by what's happened," she said.
"It's still early recovery, it's only been a week, but I'm impressing the doctors."
Ms Chard has been enduring physiotherapy and has already had "lots of drips and drains removed".
"The pain is bad but it's going to be worth it as every day I notice more things that have improved. Like, I can actually take a deep breath now - I haven't done that for a long time, or hold my breath," she said.
"It's just amazing, even food tastes good again."
A woman has paid an emotional tribute to the family of a donor who has given her "future" back.