  The mechanisms producing fast variability of the $\gamma$-ray emission in
active galactic nuclei are under debate. The MAGIC telescopes detected a fast
very high energy (VHE, E$>100$ GeV) $\gamma$-ray flare from BL Lacertae on 2015
June 15. The flare had a maximum flux of $(1.5\pm 0.3)\times 10^{-10}$ photons
cm$^{-2}$ s$^{-1}$ and halving time of $26\pm8$ minutes. The MAGIC observations
were triggered by a high state in the optical and high energy (HE, E$>100$ MeV)
$\gamma$-ray bands. In this paper we present the MAGIC VHE $\gamma$-ray data
together with multiwavelength data from radio, optical, X-rays, and HE $\gamma$
rays from 2015 May 1 to July 31. Well-sampled multiwavelength data allow us to
study the variability in detail and compare it to the other epochs when fast
VHE $\gamma$-ray flares have been detected from this source. Interestingly, we
find that the behaviour in radio, optical, X-rays and HE $\gamma$-rays is very
similar to two other observed VHE $\gamma$-ray flares. In particular, also
during this flare there was an indication of rotation of the optical
polarization angle and of activity at the 43\,GHz core. These repeating
patterns indicate a connection between the three events. We also test modelling
of the spectral energy distribution, based on constraints from the light curves
and VLBA observations, with two different geometrical setups of two-zone
inverse Compton models. In addition we model the $\gamma$-ray data with the
star-jet interaction model. We find that all of the tested emission models are
compatible with the fast VHE $\gamma$-ray flare, but all have some tension with
the multiwavelength observations.
