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Prince Harry and Meghan Markle Enjoy Texas BBQ Date, Where Harry Joked About Posing with a 'Royal' Portrait (Exclusive)

"They let us know that she wanted to come by, but did not know Harry was coming," la Barbecue Director of Operations Cory Rivademar tells PEOPLE exclusively

<p>Cory Rivademar/@coryriv/@labarbecue</p> Prince Harry and Meghan Markle pose with Allison "Ali" Clem, la Barbecue owner/operator

Cory Rivademar/@coryriv/@labarbecue

Prince Harry and Meghan Markle pose with Allison "Ali" Clem, la Barbecue owner/operator

Prince Harry and Meghan Markle couldn't take a trip to Austin, Texas, without trying some barbecue!

The couple visited the city for the SXSW Conference, where Meghan was a panelist with Brooke ShieldsKatie Couric, author/sociologist Nancy Wang Yuen and moderator Errin Haines.

Prince Harry sat in the crowd as the women participated in an International Women's Day panel called "Breaking Barriers, Shaping Narratives: How Women Lead On and Off the Screen."

Following the event, the couple visited la Barbecue.

<p>Cory Rivademar/@coryriv/@labarbecue</p> Prince Harry and Meghan Markle speak with Allison "Ali" Clem

Cory Rivademar/@coryriv/@labarbecue

Prince Harry and Meghan Markle speak with Allison "Ali" Clem

Related: Meghan Markle and Prince Harry Step Out for Dinner in Austin at Spot Linked to Their First Date (Exclusive)

"Their visit was a scheduled thing. They let us know that she wanted to come by, but did not know Harry was coming," Director of Operations Cory Rivademar exclusively tells PEOPLE. "They came in, and they toured the pits with Frankie, who is the pit guy, and talked about how hot it was around the pits, which is funny because this is Texas, and actually, it can be much hotter than today."

Rivademar says that they ordered brisket and sausages and were "absolutely lovely" as they took pictures with staff and other patrons since the restaurant remained open to the public.

She says that Prince Harry was fond of a mural of British rocker Freddie Mercury dressed as Queen Elizabeth near a unisex bathroom and said, "We should take a picture in front of this."

<p>Ali Clem</p> Freddy Mercury dressed as the Queen mural at la Barbecue

Ali Clem

Freddy Mercury dressed as the Queen mural at la Barbecue

Related: Meghan Markle Says Online 'Bullying' Peaked While Pregnant with Archie and Lili: 'It's Not Catty, It's Cruel'

According to Rivademar, Allison Clem, who goes by Ali and is the owner and operator of la Barbecue, jokingly responded to him by saying, "I think you are in enough trouble as it is," to which he laughed.

Rivademar says that after the couple left, she received a text from Meghan's representatives saying that it was the best BBQ they'd ever had.

"I thought they seemed happy and sweet, he's very lovely. She spoke about their kid loving the new Disney movie, Wish. Very genuine and very loving. Happy couple. Nice to people who didn't even know what was going on," says Rivademar.

At Friday's panel, Meghan spoke candidly about the support she has received from her "incredible partner."

<p>Cory Rivademar/@coryriv/@labarbecue</p> Prince Harry and Meghan Markle take a tour of la Barbecue

Cory Rivademar/@coryriv/@labarbecue

Prince Harry and Meghan Markle take a tour of la Barbecue

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"I'm fortunate in that, among the privileges I have in my life, I have an incredible partner," Meghan said. "My husband is such a hands-on dad and such a supporter of me and my family. That I don't take for granted. That is a real blessing," she said, noting that he is “such a supporter of me and my family."

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