Property B conjecture for expansions in completions of global function fields

Let $K$ be a global function field with normalized valuation $v$, let $K_v$ be its completion, and let $\pi\in K_v$ satisfy $v(\pi)>0$. Let $A_v$ be the completion of the valuation ring and let $\Gamma\subset A_v$ be a complete set of representatives of $A_v/\pi A_v$. An expansion with respect to $(\Gamma,\pi)$ is an expression

$$x=\sum_{n\geq m}a_n\pi^n,$$

with $a_n\in\Gamma$. Property B conjecture. The pair $(\Gamma,\pi)$ has property $B$ if and only if $\pi$ and every element of $\Gamma$ are algebraic over $K$. This is presented as a conjectural characterization of property B; the supplied text gives no resolution of the conjecture.