Lindsay Lohan Celebrates Freaky Friday Costar Jamie Lee Curtis' Oscars 2023 Win: 'Congrats!'

James Gourley/Getty; Arturo Holmes/Getty Lindsay Lohan; Jamie Lee Curtis

Lindsay Lohan is over the moon for Jamie Lee Curtis!

Lohan, 36, celebrated her Freaky Friday costar's big win at the Oscars 2023 on Instagram Sunday night, sharing a post from Variety that announced Curtis, 64, had won Best Supporting Actress for her role in Everything Everywhere All at Once.

Along with tagging Curtis in her Instagram Story post, Lohan left a string of party-horn and red-heart emojis, plus a "CONGRATS" GIF.

Also celebrating from afar was Demi Moore. Moore, 60, captioned a festive photo that also included Paris Jackson and Jaimie Alexander, "Congratulations! We love you, Jamie!!"

Still clearly on cloud nine after her first-ever Academy Award nomination and win, Curtis shared a photo of herself on Monday morning, gleefully holding her trophy the night before as she waited for it to be engraved.

"Apparently, it's not real until they put your name on it," she joked in the caption, adding, "TO EVERYONE EVERYWHERE ALL AT ONCE ... WE WON TOGETHER."

Never miss a story — sign up for PEOPLE's free daily newsletter to stay up-to-date on the best of what PEOPLE has to offer, from juicy celebrity news to compelling human-interest stories.

Lindsay Lohan/Instagram Lindsay Lohan's Instagram Story post

RELATED GALLERY: 5 History-Making Moments from the 2023 Oscars

The longtime Hollywood star's first Oscar for Best Supporting Actress is especially poignant, as it's the same award her actress mother, Janet Leigh, was nominated for in 1960.

In her acceptance speech on Sunday at the Dolby Theatre in Los Angeles, Curtis doled out thanks for the "hundreds of people" who helped her on her journey to the Oscars stage.

"To all of the people who have supported the genre movies I have made all these years, the thousands and hundreds of thousands of people, we just won an Oscar together!" she said, in addition to individually thanking her husband, daughters, agents and her film's directors, the Daniels (Daniel Scheinert and Daniel Kwan).

Curtis finished her acceptance speech by celebrating her late Oscar-nominated parents, Leigh and Tony Curtis, and exclaiming "I just won an Oscar!" before walking off the stage with her golden statue.

RELATED VIDEO: Jamie Lee Curtis Thanks Her "Beautiful Husband" and "People Who Love Genre Movies" as She Wins at Oscars 2023

Curtis will next appear in the upcoming films Borderlands and Haunted Mansion, playing the mysterious Madame Leota in the latter Disney live-action remake adaptation of the famed park attraction.

And last month, she also hinted at a sequel to the classic 2003 Disney film Freaky Friday, in which she and Lohan, who played her character's daughter, swap bodies and lives. It is the third film adaptation of Mary Rodgers' 1972 novel of the same name.

"It's going to happen," Curtis told Variety at the Producers Guild Awards. "Without saying there's anything officially happening, I'm looking at you in this moment and saying, 'Of course it's going to happen.' It's going to happen."

Back in November 2022, the star told PEOPLE, "There would be nothing I would love more, honestly, than to be able to work with [Lohan] again, share our time again, and now be able to share it at this age with both of us 20 years older, or whatever we are."

The Oscars aired live on ABC Sunday, March 12, at 8 p.m. ET.