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It's a children's story, I think. I read it when I was a kid at any rate.
It involves a young boy going to visit his grandmother who lives on the moon (or another planet or something). Instead of actually going to the other place, what people do is have their personalities implanted (using some kind of futuristing cassette tape I think) into dolls that look exactly like them so that they "travel" to the other place without having to leave Earth. I'm pretty sure there's some sort of criminal activity going on, because I remember that in the end it turned out that the grandmother wasn't the grandmother at all but someone's personality in a grandmother-looking doll, and the real grandma had been kidnapped and was being held prisoner while they used her doll to hide their identity. Almost like a Red Riding Hood story, but science fictionalized and starring a boy instead of a girl. There might have even been two kids, a boy and a girl.
Hopefully that was a decent enough description. Anyone think it sounds familiar?