"They prepared Archie by talking a lot about the baby," a source tells PEOPLE

Meghan Markle and Prince Harry's daughter has arrived — and Archie couldn't be more excited for his new role as big brother!

With Lilibet Diana's birth on June 4, Archie "is very happy to have a little sister," a spokesperson for the couple tells PEOPLE in this week's cover story.

"They prepared Archie by talking a lot about the baby. He is too little to understand though," a source adds. "He is big enough though that he is now starting to have his own life too. He enjoys preschool and outdoor activities. He will have a fun summer."

The source continues, "Meghan and Harry are also taking time off to focus on their family."

Archie will likely call his sister by the nickname "Lili," like his parents. The moniker has a sweet tie to Meghan's mom Doria Ragland, who lovingly gave Meghan the childhood nickname "Flower." In a blog post on her now-defunct lifestyle site, The Tig, the Duchess of Sussex shared her nicknames, writing, "Meg, MM, M&M, and Flower (which my mom has called me since I was little)."

Archie, who turned 2 last month, was at the center of Prince Harry and Meghan's baby announcement earlier this year. "We can confirm that Archie is going to be a big brother. The Duke and Duchess of Sussex are overjoyed to be expecting their second child," a spokesperson for the couple told PEOPLE on Valentine's Day.

Archie also appeared in a black and white snap from the couple's maternity photo shoot as he was held in Meghan's arms with his face pressed into Harry's chest.

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Prince Harry, Meghan Markle
Prince Harry, Meghan Markle and Archie
| Credit: Toby Melville/Samir Hussein/WireImage

Archie will soon be showing his little sister all of his favorite ways to spend time in California, from walks on the beach to playing with the family's two dogs, who are Archie's "best friends." 

"To have outdoor space where I can go for walks with Archie and we go for walks as a family and with the dogs. You know, we go on hikes or go down to the beach, which is so close," Harry told Oprah Winfrey during their interview, which aired in March, about family life in Montecito.

Listen below to our daily podcast PEOPLE Every Day for more on Prince Harry and Meghan Markle's new daughter, Lilibet Diana. 

"The highlight for me is sticking him on the back of the bicycle in his little baby seat and taking him on bike rides is something which I never was able to do when I was young. I can see him on the back, and he's got his arms out, chatting: 'Palm tree?' House?' " Queen Elizabeth's grandson recalled.

Meghan Markle and Prince Harry
Meghan Markle and Prince Harry
| Credit: Samir Hussein/WireImage

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Meghan, 39, and Harry, 36, took to their Archewell Foundation website to share a personal message upon sharing news of Lili's arrival: "On June 4th, we were blessed with the arrival of our daughter, Lili. She is more than we could have ever imagined, and we remain grateful for the love and prayers we've felt from across the globe. Thank you for your continued kindness and support during this very special time for our family."