Interacting Fock space versus full Fock module

We present several examples where moments of creators and annihilators on an {\it interacting Fock space} may be realized as moments of creators and annihilators on a {\it full Fock module}. Motivated by this experience we answer the question, wether such a possibility exists for arbitrary interacting Fock spaces, in the affirmative sense. Finally, we consider a subcategory of interacting Fock spaces which are embeddable into a usual Fock space. We see that a creator $a^*(f)$ on the interacting Fock space is represented by an operator $\varkappa\ell^*(f)$, where $\ell^*(f)$ is a usual creator on the full Fock space and $\varkappa$ is an operator which does not change the number of particles. In the picture of Hilbert modules the one-particle sector is replaced by a two-sided module over an algebra which contains $\varkappa$. Therefore, $\varkappa$ may be absorbed into the creator, so that we are concerned with a usual creator. However, this creator does not act on a Fock space, but rather on a Fock module.