We argue that a large region of so far unconstrained parameter space for axion-like particles (ALPs), where their couplings to the Standard Model are of order $(0.01!-!1),mbox{TeV}^{-1}$, can be explored by searches for the exotic Higgs decays $hto Za$ and $hto aa$ in Run-2 of the LHC. Almost the complete region in which ALPs can explain the anomalous magnetic moment of the muon can be probed by searches for these decays with subsequent decay $atogammagamma$, even if the relevant couplings are loop suppressed and the $atogammagamma$ branching ratio is less than~1.
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