In the recent publication [1] the spin vertex was introduced as a new approach for computing three-point functions in N = 4 SYM. In this note we consider the BMN limit of the spin vertex for scalar excitations and show that it reproduces the string vertex in the light-cone string field theory which describes the string interactions in the pp-wave background at the leading order of λ expansion. This is achieved by introducing a polynomial representation for the spin vertex. We derive the Neumann

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... coefficients from the spin vertex at weak coupling and show they match with the Neumann coefficients from the string field theory.