Using molecular dynamics simulation of a standard coarse-grained polymer glass model we investigate by means of the stress-fluctuation formalism the shear modulus $mu$ as a function of temperature $T$ and sampling time $Delta t$. While the ensemble-averaged modulus $mu(T)$ is found to decrease continuously for all $Delta t$ sampled, its standard deviation $delta mu(T)$ is non-monotonous with a striking peak at the glass transition. Confirming the effective time-translational invariance of our systems, $mu(Delta t)$ can be understood using a weighted integral over the shear-stress relaxation modulus $G(t)$. While the crossover of $mu(T)$ gets sharper with increasing $Delta t$, the peak of $delta mu(T)$ becomes more singular. % It is thus elusive to predict the modulus of a single configuration at the glass transition.
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