Perhaps the Doctor recreates it and builds one himself. Another thought was that the one he gives her is the one he gets from her in "Forest of the Dead", becoming a paradox.

it is possible that the one given to river is the old one repaired with some major improvements, I doubt he just disguarded it. However if I remember correctly the book and the screwdriver were left in the library near where the Doctor and Donna looked out over the library and asked why it was so quiet at the beginning of the tw parter

River told 10 that the screwdriver she had was a future version of his. She didn't say which future version (spoilers). Probably, its origin is still in the Doctor's future.

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