For a marked surface Sigma and a semisimple algebraic group G of adjoint type, we study the Wilson line morphism g_{[c]}:{mathcal {P} }_{G,Sigma } rightarrow G associated with the homotopy class of an arc c connecting boundary intervals of Sigma , which is the comparison element of pinnings via parallel-transport. The matrix coefficients of the Wilson lines give a generating set of the function algebra mathcal {O}({mathcal {P} }_{G,Sigma }) when Sigma has no punctures. The Wilson lines have the multiplicative nature with respect to the gluing morphisms introduced by Goncharov–Shen [18], hence can be decomposed into triangular pieces with respect to a given ideal triangulation of Sigma . We show that the matrix coefficients c_{f,v}^V(g_{[c]}) give Laurent polynomials with positive integral coefficients in the Goncharov–Shen coordinate system associated with any decorated triangulation of Sigma , for suitable f and v.