  As one of the consequences of the black-hole "no-hair" theorem in general
relativity (GR), the multipolar structure of the radiation (i.e. different
spherical harmonic modes) from a merging quasi-circular binary black hole (BBH)
is fully determined by the intrinsic parameters (i.e. the masses and spins of
the companion black holes). In Refs. [1,2], we have formulated an efficient
test named `higher-modes consistency test' to check for the consistency of the
observed gravitational-wave (GW) signal with the expected multipolar structure
of radiation from BBHs in GR. Detection of the high-mass-ratio merger of
GW190814 enables the observation of spherical harmonic modes beyond the
dominant $(\ell, m) = (2,\pm2)$ mode; thereby providing a unique opportunity to
perform the `higher-modes consistency test'. Using different state-of-art
waveform models (IMRPhenomXPHM, IMRPhenomXHM, IMRPhenomHM and SEONNRv4HM_ROM),
we show that GW190814 strongly favors the "no-hair" hypothesis in GR over a
hypothesis that assumes generic deviation from the multipolar structure of the
radiation by a Bayes factor of $\rm log_{e}\mathcal{B}\sim8$. We further
investigate any potential systematic errors arising as a result of different
waveform modeling choices as well as due to neglecting many higher order modes.
We find that, if the waveform model includes only $(\ell, m) = (3,\pm3)$ mode
in its higher harmonics, the same event may reject the `no-hair' hypothesis in
GR when the detector sensitivity improves by a factor of $12.5$. Our analysis,
therefore, provides motivation to include as many higher order modes as
possible in future waveform models.
