  Context. Kepler observations revealed a brown dwarf eclipsing the M-type star
LHS 6343 A with a period of 12.71 days. In addition, an out-of-eclipse light
modulation with the same period and a relative semi-amplitude of 2 x 10^-4 was
observed showing an almost constant phase lag to the eclipses produced by the
brown dwarf. In a previous work, we concluded that this was due to the light
modulation induced by photospheric active regions in LHS 6343 A. Aims. In the
present work, we prove that most of the out-of-eclipse light modulation is
caused by the Doppler-beaming induced by the orbital motion of the primary
star. Methods. We introduce a model of the Doppler-beaming for an eccentric
orbit and also considered the ellipsoidal effect. The data were fitted using a
Bayesian approach implemented through a Monte Carlo Markov chain method. Model
residuals were analysed by searching for periodicities using a Lomb-Scargle
periodogram. Results. For the first seven quarters of Kepler observations and
the orbit previously derived from the radial velocity measurements, we show
that the light modulation of the system outside eclipses is dominated by the
Doppler-beaming effect. A period search performed on the residuals shows a
significant periodicity of 42.5 +- 3.2 days with a false-alarm probability of 5
x 10^-4, probably associated with the rotational modulation of the primary
component.
