Another source added that Harry was determined to make sure Queen Elizabeth and Markle had a close bond, so he requested a sit-down with his grandmother when he knew his romance with Markle was getting serious.
The royal couple joined the cast of West End hit Hamilton on-stage for a singalong.
Hamilton tells the story of United States founding father Alexander Hamilton, and features King George III in a scene-stealing comic role - peacocking around the stage as he expresses disbelief and frustration at America's battle for independence.
It was after the performance that Harry teased the audience as he took the stage to thank everyone for contributing to the organisation, of which he is a patron.
Meghan, who has watched the show both sides of the Atlantic while Harry has seen it once in London, said audiences' responses are "so different" between the United Kingdom and the US.
Harry's musical debut was quite brief - he literally only sang the first two words, "You say" - but the performance still stole the show and caused the audience to burst into applause.
Pierce was one of the few Suits stars who didn't attend Meghan's wedding to Prince Harry, but he reminisced about a sweet moment he shared with Meghan when they were filming her on-screen wedding for the series.
In the weeks since the May 19th royal nuptials between the newly minted Duchess and her new husband, Prince Harry, Markle's father, Thomas Markle Sr., has appeared in a number of interviews.
Harry then thanked the crowd for raising money for his charity Sentebale - which works with kids and youngsters affected by HIV in southern Africa - by attending the production.
Both had already considered the sing, but had been internet hosting the gala efficiency for Sentebale, which Harry founded with Prince Seeiso of Lesotho after the duke's hole year there.