I'm going through an exam question where I've been told that the samples $f(kT)$ of the following function \begin{equation}{F\left(z\right)=\frac{1}{1-0.819z^{-1}}} \end{equation} are applied to a discrete system with the pulse transfer function
$$\text{G}\left(z\right)=\frac{C(z)}{F(z)}=\frac{T}{2}{\left(\frac{1+z^{-1}}{1-z^{-1}}\right)}\quad\text{where}\quad T = 0.1\textrm{ s}$$
I'm then asked to determine the final value of the output of the system. I know that the final value theorem states
\begin{equation}{\lim_{k\to\infty}f\left(kt\right)=\lim_{z\to1}\left(1-z^{-1}\right)\cdot F\left(\text{z}\right)} \end{equation}
but how do I obtain a value of $F(z)$? I'm not sure how the two equations above are manipulated to obtain the $F(z)$ I should be using the final value theorem with.