We consider the $d$-dimensional threshold voter model. It is
known that, except in the one-dimensional nearest-neighbor case, coexistence
occurs (nontrivial invariant measures exist). In fact, there is a nontrivial
limit $\eta_\infty^{1/2}$ obtained by starting from the product measure with
density 1/2. We show that in these coexistent cases,
\eta_t \Rightarrow \alpha\delta_0 + \beta\delta_1 + (1 - \alpha -
\beta)\eta^{1/2}_\infty \quad\text{as $t \to \infty$},
where $\alpha=P(\tau_0<\infty), \beta=P(\tau_1<\infty),
\tau_0$ and $\tau_1$ are the first hitting times of the all-zero and all-one
configurations, respectively, and $\Rightarrow$ denotes weak convergence.