The queen sits by his side cradling a young Prince Louis in the photo, which was taken in 2018 at their royal residence in Scotland, Balmoral Castle.
Prince Charles' account shared an older black-and-white image of the father and son posing on horseback with polo mallets in their hands.
On Thursday the Prince of Wales and his wife, Camilla, visited a selection of flowers and condolence messages left by the public that had been moved from outside Buckingham Palace to private gardens at Marlborough House, another royal building, due to Covid-19 restrictions.
Crowds flocked outside royal residences, including Buckingham Palace in central London and Windsor Castle about 25 miles away, to lay floral tributes and hand-written notes in the wake of Philip’s death.
Princess Eugenie shared her own remembrance of her "dearest Grandpa" on her personal Instagram page, stating that he "would be so touched by all the tributes that have been shared."
Four days after the death of her husband, Queen Elizabeth returned to some royal duties earlier this week.The queen hosted a ceremony on Tuesday to mark the retirement of her household's most senior official.
Her daughter, Princess Anne, 70, was seen in public for the first time on Wednesday dressed in black and wearing sunglasses as she arrived at the Royal Yacht Squadron, a sailing club on the Isle of Wight.
"My father has been my teacher, my supporter and my critic," Anne, the Princess Royal, said in a statement on Sunday. "But mostly it is his example of a life well lived and service freely given that I most wanted to emulate."
Rehearsals for the scaled back funeral were underway, with military parades and bands practicing for the event.
Attendance will be limited to 30 people due to coronavirus restrictions in England. A ceremonial procession will take place followed by a service at St George’s Chapel in Windsor.
Prince Harry has returned to the U.K. from his new home in the United States for the event.