  Let p be a prime and T a lattice inside a semi-stable representation V. We
prove that Kisin modules associated to T by selecting different uniformizers
are isomorphic after tensoring a subring in W(R). As consequences, we show that
several lattices inside the filtered (phi, N)-module of V constructed from
Kisin modules are independent on the choice of uniformizers. Finally we use a
similar strategy to show that the Wach module can be recovered from the
(\varphi, \hat G)-module associated to T when V is crystalline and the base
field is unramified.
