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Steve Parsons – WPA Pool/Getty Queen Elizabeth and Prince Harry in 2019

Prince Harry is cherishing the moments he and his family had with his “granny” Queen Elizabeth.

The Duke of Sussex, 38, reflects on his “special relationship” with the history-making monarch, who died in September at age 96, in his memoir Spare, out Tuesday. Speaking exclusively with PEOPLE in this week’s cover story, Prince Harry shares how he’ll remember her.

“My grandmother and I were very close, and we very much did have a special relationship,” he says. “I miss her dearly, as well as her cheeky sense of humor and quick wit.”

“I’m also really happy for her. She lived a full life and is now reunited with her husband,” Harry continues, recalling his grandfather Prince Philip, who died in April 2021.

“I will forever cherish every memory I had with her, especially the times she spent with my children,” he adds of his two kids with Meghan Markle — son Archie Harrison, 3, and daughter Lilibet Diana, 19 months.

RELATED: Prince Harry Tells PEOPLE: Spare Is a Raw Account of the ‘Good, the Bad and Everything in Between’

Tim Graham Picture Library/Getty Queen Elizabeth and Prince Harry

In Spare, Prince Harry reflects on when Archie and Lilibet (whose name comes from Queen Elizabeth’s family nickname stemming from her childhood) met their great-grandmother in June 2021. The family had traveled to the U.K. from their California home for the monarch’s Platinum Jubilee celebrations, marking her 70 years on the throne.

Harry recalled Archie “making deep, chivalrous bows” while Lili was “cuddling the monarch’s shins.”

For more from PEOPLE‘s exclusive interview with Harry, check out this week’s issue, on newsstands Friday

“Sweetest children, Granny said, sounding bemused,” he wrote in the book. “She’d expected them to be a bit more . . . American, I think? Meaning, in her mind, more rambunctious.”

Jenna Jones

While Prince Harry candidly explores his fractured relationship with the royals, including his father King Charles and brother Prince William, in his new memoir, he tells PEOPLE that he hopes for reconciliation as well as for his children to have meaningful relationships with his family members.

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PENGUIN RANDOM HOUSE The book jacket of Prince Harry’s memoir ‘Spare’

“I’ve said before that I’ve wanted a family, not an institution—so of course, I would love nothing more than for our children to have relationships with members of my family, and they do with some, which brings me great joy,” he says.

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