“One thing about the Queen is she has to manage being a grandmother but also how it affects the wider institution,” a royal insider says in the new issue of PEOPLE Royals

Prince Harry may have stepped back from his royal role, but he remains close to Queen Elizabeth.

Throughout the turmoil of Harry and wife Meghan Markle’s departure from royal life — which has seen rifts between the couple and other royal family members, including Prince William — the Duke of Sussex has made sure his relationship with his grandmother has remained intact.

Harry and the Queen keep up to date on his life and his children, Archie and Lilibet, via video calls. And he dropped in on the Queen at her Windsor Castle home in April while en route to the Invictus Games in The Netherlands.

He also introduced his 1-year-old daughter Lilibet (the Queen’s namesake!) to the monarch when the family was in the U.K. for the Platinum Jubilee celebrations earlier this month.

For her part, the Queen has had to steer a tricky course between sympathy for the couple and firmness in favor of her role as monarch.

“One thing about the Queen is she has to manage being a grandmother but also how it affects the wider institution,” a royal insider says in the latest PEOPLE Royals, out Friday.

Queen Elizabeth and Prince Harry. Chris Jackson/Getty

Few public moments illustrate Harry’s bond with his grandmother the Queen like the time she joined her grandson for a playful video to tout the Invictus Games in 2016.

Seated on a floral sofa in Windsor Castle, Harry leaned into Queen Elizabeth and showed her a short video on his phone. On it were then-President Barack Obama and First Lady Michelle Obama teasing him about the upcoming Invictus Games. they cheekily said the U.S. was going to win big at the Paralympic-style games that Harry launched years ago for armed forces members — and one of the servicemen surrounding the Obamas sent out a triumphant “Boom” to underscore the boast.

But Harry and his grandmother had other ideas: As cameras rolled, the Queen shrugged her shoulders and said in classic understatement: “Boom, really? Please.”

Six years later it’s clear there are few, if any, members of the Queen’s extended family who would have the confidence and the humor to ask the Queen to take part in such a stunt.

Queen Elizabeth and Prince Harry. John Shelley Collection/Avalon/Getty

Harry’s doing so underlined both the respect between him and his grandmother and her willingness to show a different side of herself for him — in front of the world.

“If Harry asks, the Queen would say yes— as she adores him,” a friend has said of the bond between the monarch and the Duke of Sussex.