  Let F be a non-archimedean local field. The construction of Lubin-Tate
$(\phi_q, \Gamma)$-modules attached to p-adic representations of $G_F$ depends
on the choice of a uniformizer of F. In this paper, we give a description of a
functor which relates categories of overconvergent Lubin-Tate $(\phi_q,
\Gamma)$-modules for different uniformizers. Further, we study this functor
more explicitly for 2-dimensional trianguline representations.
