LOTR: Did Arwen Lose Her Immortality?

gamerant.com:

In The Lord of the Rings, Arwen (an Elf maiden) and Aragorn (a human man who was one of the Dúnedain—a descendant of the Númenóreans), were in love. Though the Dúnedain were blessed with long life and slow aging, they were still mortal. On the other hand, Elves are immortal beings that never succumb to old age. They can even recover from wounds that would be fatal to Man. Although they can be killed in battle, all Elves' spirits go to The Halls of Mandos when they die.

In the books, Arwen possesses a stone called the Elfstone, which was a green gem on an eagle-shaped brooch that had the light of the Sun within it. Looking through the gem would cause the viewer to see all that was now old as young and new again. But in the movies, this stone was replaced by the Evenstar (which was not in the books, except as a nickname for Arwen) to show how Arwen was one of the last Elves to live in Middle Earth, and she was as bright and light as the star. The Evanstar was most likely used to replace both the Elfstone and the «white gem like a star» on a silver chain that Arwen gives to Frodo after he finally destroys the Ring as a gift to comfort him through troubling times (in the books).

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But in the movies, the Evenstar was given to Aragorn by Arwen to show how she would forsake her immortal life to be with her one true love—saying, «I would rather spend one lifetime with you than face all the ages of this world alone.» Many first-time viewers might have thought that this necklace was the source of Arwen's immortality, and that by giving it to Aragorn, she was giving him an immortal life and giving up her own. Aragorn even says «you cannot give me this» to which Arwen replies «it is mine to