L-infinity algebra structure maps can be regarded as degree -1 elements in the symmetric brace algebra B_*(V)=\oplus Hom(V^{\otimes n},V)^a that satisfy a relation in this algebra. We will show how certain degree 0 elements in B_*(V) can be regarded as L-infinity algebra morphisms between different L-infinity algebra structures on V with the relations given by symmetric brace algebra actions. To extend these ideas to L-infinity algebra morphisms from V to W, one has to introduce the concept of modules over symmetric brace algebras. The graded vector space B_*(W,V)=\oplus Hom(V^{\otimes n},W)^a has to have the structure of a left B_*(W) module as well as the structure of a right B_*(V) module.