Manolescu and Woodward defined homology groups associated to a closed connected oriented 3-manifold, called symplectic instanton homology, using Lagrangian Floer homology inside a moduli space of flat SU(2)-connexions associated to a punctured Heegaard surface. Using Wehrheim and Woodward's "Floer field theory" and pseudo-holomorphic quilts, I will show that these groups only depend on the choice of a basepoint, and will define maps associated to a smooth 4-dimensional cobordism equipped with a path.