We apply the theory of φ-coordinated modules, developed by H.-S. Li, to the Etingof–Kazhdan quantum affine vertex algebra associated with the trigonometric R-matrix of type A. We prove, for a certain associate φ of the one-dimensional additive formal group, that any φ-coordinated module for the level c ∈ C quantum affine vertex algebra is naturally equipped with a structure of restricted level c module for the quantum affine algebra in type A and vice versa. Moreover, we show that any… Expand