This sounds intriguing. I wonder what has caused her "jigsaw memory." It's a really interesting topic to explore.
I love your use of language, by the way. It's really poetic.
Oh, Hermione's mother! That makes sense. You give her life a nightmarish quality - that sense that there is something she's forgotten, but she doesn't know what it is. It must be something similar to what people say with Alzheimer's feel.
I like the way she connects her apparent lack of children with her dreams of travel. It makes sense as an explanation when she doesn't know that she does have a daughter.
I assumed the yellow mug must have been a present from Hermione.
And that part about the wave goodbye is so sad. It always strikes me as weird how easily everybody accepts 11 year olds pretty much spending the rest of their childhood living away from their parents.
The end of this story is really emotive and I'm glad Hermione found them again.