  The photon polarization in B -> V gamma is a sensitive probe of right-handed
currents. In the time dependent decay rate of B_s -> phi gamma the coefficients
S and H in front of the sin(Delta m_s t) and the sinh(Delta Gamma_s /2 t) terms
are sensitive to those right-handed currents. As compared to the B_d system
there is a sizable width difference in B_s mesons which leads to the additional
measurable observable H. We show with a Monte Carlo simulation that the
expected resolution on S and H will be about 0.15 at the LHCb experiment for
Delta Gamma_s/Gamma_s = 0.15 and a data sample of 2 fb^{-1}. We also show that
the observable H can be measured from the untagged decay rate of B_s mesons
which has considerable experimental advantages as no flavour tag will be
required. The resolution on H is inversely proportional to the B_s width
difference Delta Gamma_s. These experimental prospects have to be compared with
the Standard Model predictions S_{phi gamma} = 0 \pm 0.002 and H_{phi \gamma} =
0.047 \pm 0.025+0.015 presented in this paper. We also give the Standard Model
prediction and the experimental sensitivity for the direct CP asymmetry in B_s
-> phi gamma.
