[en] Form factors for local spin operators of the XXZ Heisenberg spin-z finite chain are computed. Representation theory of Drinfel'd twists in terms of F-matrices for the quantum affine algebra U_q(s-circumblexl₂) in finite-dimensional modules is used to calculate scalar products of two states involving one Bethe state (leading to Gaudin formula) and to solve the quantum inverse problem for local spin operators in the finite chain. Hence, we obtain the representation of the n-spin correlation functions in terms of expectation values (in ferromagnetic reference state) of the operator entries of the quantum monodromy matrix satisfying Yang-Baxter algebra. This leads to the direct calculation of the form factors of the XXZ Heisenberg spin-! finite chain as determinants of usual functions of the parameters of the model. A two-point correlation function for adjacent sites is also derived using similar techniques