  The orbit of the outer satellite Alexhelios of (216) Kleopatra is already
constrained by adaptive-optics astrometry, obtained with the VLT/SPHERE
instrument. However, there is also a preceding occultation event in 1980
attributed to this satellite. Hereinafter, we try to link all observations,
spanning 1980--2018. We find the nominal orbit exhibits an unexplained shift by
$+60^\circ$ in the true longitude. Using both periodogram analysis and an $\ell
= 10$ multipole model suitable for the motion of mutually interacting moons
about the irregular body, we confirmed that it is not possible to adjust the
respective osculating period $P_2$. Instead, we were forced to use a model with
tidal dissipation (and increasing orbital periods) to explain the shift. We
also analyzed light curves, spanning 1977--2021, and searched for the expected
spin deceleration of Kleopatra. According to our best-fit model, the observed
period rate is $\dot P_2 = (1.8\pm 0.1)\cdot 10^{-8}\,{\rm d}\,{\rm d}^{-1}$
and the corresponding time lag $\Delta t_2 = 42\,{\rm s}$ of tides, for the
assumed value of the Love number $k_2 = 0.3$. It is the first detection of
tidal evolution for moons orbiting 100-km asteroids. The corresponding
dissipation factor $Q$ is comparable with other terrestrial bodies, albeit at a
higher loading frequency $2|\omega-n|$. We also predict a secular evolution of
the inner moon, $\dot P_1 = 5.0\cdot 10^{-8}$, as well as a spin deceleration
of Kleopatra, $\dot P_0 = 1.9\cdot 10^{-12}$. In alternative models, with moons
captured in the 3:2 mean-motion resonance or more massive moons, the respective
values of $\Delta t_2$ are a factor of 2--3 lower. Future astrometric
observations by direct imaging or occultations should allow to distinguish
between these models, which is important for the internal structure and
mechanical properties of (216) Kleopatra.
