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These are excellent questions that someone who knows more about her life could probably answer better than I can, but to give you a few broad strokes ...
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How did the imposter convince her visiting relatives she was their sister, aunt? The name of the house next door, her first pet, the old lady who used to chased them away, what her father used to whistle and other past memories? Any suspicion from those relatives and it would be incredibly easy to catch the imposter out and impossible for the imposter to protect against. "Remember Sergio our neighbour, he died, please pray for him". The neighbour's name was Noel. A huge risk. The relatives would tell other relatives and word would get out.
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Sure, her relatives could have figured out that she was an imposter in about 30 seconds flat if:
1) They had wanted to go visit her, and
2) They had been given permission to visit her, and also
3) They had done a test like what you described to see if it was really her.
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I think each of those conditions is unlikely. My impression is that Sr. Lucy was kept for most of her life in a strange sort of incommunicado. No one, to my understanding was allowed to visit her, probably including her own family. That only confirms suspicions about this. Even if her family had visited her, unless they suspected some fraud, they would not have asked her such questions.
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What about the sisters who spent 30 years with the real sister Lucia in the convent? Surely at some point they would bump into the fake Lucia. If you think the difference is that obvious, from several pictures, then surely they would have known from two people in the flesh in 3D and colour.
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I think this is why the blogger quoted earlier posited that the switch was made when Sr. Lucy was transferred to a different convent. That would eliminate the need to have someone new show up in a convent claiming to be Sr. Lucy, which the other nuns would know was not the case. In any case, we really don't know under what conditions Sr. Lucy lived in that convent. She could have been confined to her room, so that the other nuns may not have known her all that well. Or, if some of the nuns said they thought Sr. Lucy had been replaced with someone else, they could have been told they were crazy and also told to not talk about their ideas. Nuns spend their whole lives in an atmosphere of humility and obedience, and if a nun were told something like that, I can easily see her just keeping her mouth shut and trusting her superiors.
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What is in it for the actress? Nuns are in convents living lives shut away from the world for their eternal salvation. The actress would know she was perpetrating a fɾαυd. Why would she be motivated to commit her entire adult life to that? What about her parents, sisters, brother, friends? She effectively had to cut off all her past forever. Who would do that and for what reward?
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My personal suspicion is that they got some nun who had lost her faith or her morals or both to agree to impersonate Sr. Lucy. I agree that convincing a person from the world to become a nun to pretend to be Sr. Lucy would never have worked. They could easily have found some nun who had become a modernist or lost her faith, but who wanted to continue living in the convent because she had no real way to make a living in the world, and decided to hang on to the security and stability of convent life, but without any supernatural spirit behind it. How would they convince such a person to play the role? How about bribing her with photographs taken with John Paul 2? How about all the glory and honor the world would have given her as a supposed seer of Our Lady? All the photo opportunities she would have had with famous people? That by itself would be enough to convince someone who wasn't giving up a whole lot to begin with, but they could easily have given her a more comfortable room in the convent, better food, fiction novels if she wanted them, and numerous other things.
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I think it's important to remember in all of this that of all people in the world Carmelite nuns are the most likely to give people the benefit of the doubt, to obey superiors, to assume the best, to mind their own business even if something really looks "off" to them, to keep their mouth shut if told, and to just let things alone if they don't know what else to do. What motive would any of them have to raise some sort of alarm about a fake Sr. Lucy if their own priest (probably) had gaslighted them when they told him they thought Sr. Lucy was different or gone?
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There are few environments more controlled than a Carmelite convent of nuns, and few environments in which it would be easier to pull of something like this.