  We will give a proof of the following fact. If $\mathfrak{A}_1$ and
$\mathfrak{A}_2$, $\tilde \eta_1$ and $\tilde \eta_2$, $\xi_1$ and $\xi_2$ are
two examples of filtered probability spaces, time homogeneous compensated
Poisson random measures, and progressively measurable Banach space valued
processes such that the laws on $L^p([0,T],{L}^{p}(Z,\nu ;E))\times
\CM_I([0,T]\times Z)$ of the pairs $(\xi_1,\eta_1)$ and $(\xi_2,\eta_2)$ %,
$i=1,2$, are equal, and $u_1$ and $u_2$ are the corresponding stochastic
convolution processes, then the laws on $ (\DD([0,T];X)\cap L^p([0,T];B))
\times L^p([0,T],{L}^{p}(Z,\nu ;E))\times \CM_I([0,T]\times Z) $, where $B
\subset E \subset X$, of the triples $(u_i,\xi_i,\eta_i)$, $i=1,2$, are equal
as well. By $\DD([0,T];X)$ we denote the
  Skorokhod space of $X$-valued processes.
