Lubin–Tate change of series

If $f$ and $g$ are Lubin–Tate series for the same uniformizer, there is a unique strict isomorphism $h:{\mathcal{F}}_f\to {\mathcal{F}}_g$ satisfying $h\circ f=g\circ h$ and $h(X)\equiv X(\mathrm{mod}{X}^2)$.