Speaking yesterday about the transplant at The Freeman Hospital. Paul's aunt Carmel Rankin said: "It's a wee miracle!"
"He's doing fine, there's been great improvement since the operation, doctors are impressed with how quick he seems to be recovering.
"Today they have him sitting out on a chair, and taking small steps, although he's retaining a lot of fluid since the operation. But he just wants to get home," his aunt added.
But Paul's Transplant Co-Ordinator, Dr. Lynn Holt, said the little boy almost missed out on his new heart due to a shortage of private jets because of the World Cup.
"This nearly didn't happen, we couldn't get a plane to fly my team there with the new heart. All the jets were so busy with the World Cup, no-one could get a private flight.
"We could have given up, but the donor family were so desperately keen to get their organ used, we ended up getting scheduled flights instead."
"People do have private planes, but just don't realise how much we might need them. If they knew the situation, maybe they'd offer them to us when available," Dr. Holt added.
Paul suffers from a severe heart condition called dilated cardiomyopathy and was fitted with a pacemaker at only five months old. For his long term survival, a heart transplant was his only hope.
Paul's devoted parents, Bella and Paul Donnelly - who first highlighted their son's plight in the Derry Journal last year - have been keeping a vigil at his bedside.
"They were really scared," Mrs. Rankin said, "He'd been called up for an operation three weeks ago, but that heart turned out to have a fault in it.
"Then, on Thursday morning around 7am, we got a phone call and they took him straight to Newcastle."
Mrs. Rankin said that Paul's brother and sister are also "delighted" he's finally had his transplant.
"They're happy they'll be able to play with him just like a normal boy now."
News of Paul's transplant and rapid recovery will be welcomed by the wider family circle too.
Tragedy struck the family last January, when Bella and Carmel Rankin's other sister, Annie, was killed in a house fire at her home in Galliagh. Paul's diagnosis came only a month later.
"All my parents' prayers have been answered. It's been a tough year, so this is great. They thought they would lose Paul too," Mrs. Rankin said.
"We'd like to thank all the people of Derry who supported Paul, thanks to The Derry Journal for their support too." And of course, they especially want to thank the donor's family. "It must have been such a hard decision for that family to make, but we appreciate that they have given Paul the chance to live," his aunt said.
"Paul's a fighter and whoever's heart he has, we're so grateful to them. We thought there was no hope."