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We find an explicit relation between the two known ways of generating an infinite set of local conserved charges for the string sigma model on AdS 5 × S 5 : the Bäcklund and monodromy approaches. We start by constructing the two-parameter family of Bäcklund transformations for the string with an arbitrary world-sheet metric. We then show that only for a special value of one of the parameters the solutions generated by this transformation are compatible with the Virasoro constraints. By solving the Bäcklund equations in a non-perturbative fashion, we finally show that the generating functional of the Bäcklund conservation laws is equal to a certain sum of the quasi-momenta. The positions of the quasi-momenta in the complex spectral plane are uniquely determined by the real parameter of the Bäcklund transform.

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