The reality star played a round of "Show Me Your Phone" with Jimmy Fallon

It’s not every day you get to read Kim Kardashian West‘s texts.

During an appearance on The Tonight Show Starring Jimmy Fallon on Wednesday, the Keeping Up with the Kardashians star played a round of “Show Me Your Phone.” The game is simple: The press of a button randomly selects an app from the celebrity’s phone and reveals something they must share from it.

Kardashian West, who promised she “didn’t even clean out” her phone beforehand, was up first and was forced to show the last texts between her and her husband, Kanye West.

“Okay, it’s fine, it’s so sweet,” she said before revealing a photo West, 42, had texted her of “West Lake” in Wyoming, where he just bought a ranch for their family.

“West Lake,” reads the accompanying message. “The first ranch in our family. 50 years from now this will mean so much to us.”

“I told you, it’s sweet,” said Kardashian West, 38. “He got a ranch in Wyoming and … there’s something that’s called West Lake. So he took a picture of it and that’s like, a sign. He’s so excited to maybe be moving to Wyoming. Well, not full time.”

Kim Kardashian Reveals Her Last Texts with Kanye West

A source told PEOPLE earlier this week that West has been visiting Cody, Wyoming, and “bought a ranch and is touring local elementary schools.” The insider said the property was previously known as “Monster Lake Ranch,” features panoramic views of the surrounding Rocky Mountains and comes in at just over 4,500 acres. The massive chunk of land cost him $14 million, according to TMZ.

“Kanye seems great,” the source said. “He loves Jackson Hole. He thinks it’s the perfect place to create his music.”

Kanye West and Kim Kardashian West
| Credit: Taylor Hill/FilmMagic

Kardashian West also recently told Vogue Arabia that she sees the family — which includes children Psalm, almost 4 months, Chicago, 19 months, Saint, 3½, and North, 6 — relocating to Wyoming at some point in the future.

“In my mind I’m already living in those 10 years,” she said. “I see us living on a ranch in Wyoming, occasionally going to Palm Springs and our home in Los Angeles — and becoming a lawyer.”

On The Tonight Show, she confirmed her husband’s “dream and his vision” is to move to Wyoming. “We love Wyoming, it’s always been such an amazing place,” she said.

But for now, Kardashian West said she would prefer to split their time between the new ranch and Southern California.

“I love L.A., so I envision summers, I envision some weekends [in Wyoming],” she said. “But yeah, we love it. It’s like, the prettiest place you’ve seen in your entire life. Even my sisters, everyone, we’ve had this dream of getting a ranch and just spending our summers there and getting away.”