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Continuity mistake: After Rey touches Luke's lightsaber she begins to have the vision, and when she falls to the floor the blaster is missing from the back of her belt, but after she "sees" Luke and R2 and then stands up the blaster is back again, tucked into her belt (even though Rey's having her vision of things all around her, she herself is not a vision).
Answer: The First Order already has the piece that R2-D2 was carrying as well. That is the first piece, the large piece of the map missing a small section. The second piece is carried by BB-8 and only by BB-8, the missing piece in the map. All the first order needs is that second piece, and so does the Resistance. However the Resistance needs R2-D2 to activate again so he can show them the first piece, so they can put the second piece in it.
lionhead