Disclaimer : I don't own Star Wars.
Summary : Some random woman gave young Princess Leia the Japor pendant necklace Anakin made Padme, and Darth Vader and her meet on the Death Star.
Flashback
A random Padme Naberrie's loyal to young Princess Leia : "There child, one day, it'll save your life."
The Young Alderanean Princess didn't understand then, but she would, some decades later. She took it from the random woman's hands and put it around her neck because she thought it a pretty necklace, although she didn't know it was her biological father who made it for her mother. Also, that this woman served her mother for 2 decades and they were as close as sisters. She took it right from the young princess' birth mother's neck at her funeral to give it to her little daughter whom she loved as hers.
End Flashback
Now, on board the Death Star
We were now on board the Death Star, where the actual Princess of Alderan was about to get interrogated by Lord Vader, with general Tarkin helping him. But lo, Darth Vader saw something on the Princess's neck that surprised him, the Japor Pendant necklace he once gave to his beloved. First, these thoughts raced in his mind : "How dare this rebel take it from her?" Then, because it didn't make any sense at all to him, therefore he wanted some time alone, without the general, to question her about how she got it. He thought he must have some time with her by himself, so he ordered General Tarkin aside :
"General, I think your methods aren't as efficient as they seem, since she isn't giving any information. I'll try her alone with the ways of the Force and force it out of her." That was his way of saying that he found Tarkin's ways ineffective as the general already probed her once, and she didn't let out anything.
Thus, Lord Vader ordered her to get out of her interrogation chair, and to go with him.
"Where to, my Lord?" Came the Princess's sarcastic way of calling him "My Lord."
Since her sneering didn't affect him, he just answered :
"To my chambers."
He led her there and motioned her to a seat.
"Will you do me the pleasure to sit down, Your Highness?" replied he with equal sarcasm on the "Your Highness."
"Why yes, my Lord." And she sat down.
"What shall we begin with today? The location to the Rebel Alliance's base or something else?" She taunted him.
"Not that. I wish to ask you some questions about how you got your necklace."
"What?" Princess Leia was surprised.
"You heard me, your necklace, where did you get it?"
"I won't tell you anything, you monster!"
"You won't? Then shall I force it from you?" Vader began using the Force to probe her. She got a headache from it, but hid it well from him.
"I won't give you anything!"
"The Force is strong with you, Your Highness, though I must know where it came from."
"Why?"
"Am I interrogating you, or is it the other way around?"
"Right then, fine, I will tell you since you asked so nicely". She said finally, but she didn't drop her sarcasm, because he was using more and more the Force on her until she couldn't bear it anymore.
"A random woman gave it to me when I was little, she said one day it'll save my life, I swear, that's all I know about it."
Lord Vader probed her again, she was telling the whole truth this time, and he found out why the random woman the princess mentioned it'd save her life. Because he gave it to her mother, and this Princess was his child. He saw in her mind this woman she talked about taking it from his departed wife's neck and give it to a younger Princess Leia. He had only one option : to save his child from further torture.