Fabian Bate, 9, received a personal note – written on St. James Palace letterhead and dated Oct. 13 – from Kate on Friday, and posted it on his blog.
"I was so touched by your strength of character," the Duchess writes. "I will keep my fingers crossed that your health goes from strength to strength."
Writing she will keep the boy, who has leukemia, and his parents in her "thoughts and prayers," Kate praises the work of the hospital and Fabian's "belief and positive energy."
"For us as a family it was a massive boost to know that we have someone at Kate's level sharing our journey," Fabian's father, Darrell Bate, 49, tells PEOPLE. "The thought that someone in her position would take that personal interest is a real hope-builder."
The letter arrived at the Bate household on Friday, just as Fabian returned home from an eight-day stay at the hospital. "It came special delivery with the Buckingham Palace postmark," Darrell said. "We realized it wasn't the average tax bill!"
Courtesy Fabian Bate
Fabian, who was first diagnosed with leukemia in 2006, relapsed earlier this year. A test this week will determine whether he'll be ready as early as December to receive a bone-marrow transplant from one of two sisters who've been found to be a perfect match.
"If [Kate] is going to take the trouble to follow our little family situation with everything else going on in the world, it makes Fabian feel special," his father says. "It gives him a bit more fight to be honest."