The photo shows the family walking outside the church at Sandringham for the Christmas Day service.
The royal message read, "Thank you for your thoughtful Christmas message to The Prince and Princess of Wales, Prince George, Princess Charlotte and Prince Louis."
The fan received a personalized thank-you card from Queen Consort Camilla for their Christmas wishes earlier this year.
Kate said the family's first Christmas without the Queen was emotional.
Charles' first Easter weekend as King will be marked next weekend.
The royals are expected to spend the weekend at Windsor and attend the Easter Sunday service at St George's Chapel.
Prince Harry and Meghan Markle are not expected to join the celebrations.