Warning: SPOILERS for Obi-Wan Kenobi episode 3.
Obi-Wan Kenobi episode 3 provides a perfect explanation for why Leia remembers Padme, despite the latter dying shortly after Leia was born. When Padme died at the end of Star Wars: Episode III — Revenge of the Sith, during childbirth, it created somewhat of a plot hole for Return of the Jedi. In the final installment of George Lucas' original Star Wars trilogy, Leia told Luke everything she remembered of her birth mother, but how could she have remembered in the first place? She was only an infant.
In Lucas' eyes, the only way to follow up The Empire Strikes Back's twist that Darth Vader was Luke's father was to suddenly reveal in Return of the Jedi that Leia was also his sister. But unlike Leia, Luke had no memory of his parents from when he was a child, especially not his mother — though Leia did. She told Luke that their mother was "very beautiful; kind, but sad," which tracks with Padme's depiction in the prequels, especially after Anakin Skywalker turned to the dark side in Revenge of the Sith. And now, dialogue from Obi-Wan Kenobi can explain why Leia remembered Padme.
Related: Obi-Wan Kenobi's Parents & Brother: Everything We Know
In Obi-Wan Kenobi episode 3, Leia asks Obi-Wan if he's her birth father, to which he says no. To empathize with her, he explains how Force-sensitive children are taken from their families when they are very young and are trained to become Jedi. It happened to him, so the only things he remembers about his family are his mother's shawl, his father's hands, and even a baby, who could be Obi-Wan's brother. Given both of them are strong in the Force, it's plausible that, because they're Force-sensitive, they can access fleeting memories from
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