A non-trivial test of the string vs. integrability correspondence is suggested: exact equivalence is established between strings in AdS4 x CP3 and the Gromov-Vieira all-loop integrable chain. To do that, the complete one- and two-magnon sector of each respective theory are calculated. In the single-magnon sector a direct perturbative one-loop calculation proves the validity of the dispersion law coming from the Bethe Ansatz, rather than of the one coming from the semiclassical analysis. In the two-magnon sector the full spectrum of the finite-size corrections has been calculated on the string side by us for the first time, that proves to be identical to the integrable chain spectrum. These results are interpreted by us as a confirmation of the exactness of the conjectured Gromov-Vieira Bethe Ansatz.