  The complete set of relations, which mutually express the spacelike and
timelike kernel functions for the hadronic vacuum polarization contribution to
the muon anomalous magnetic moment $a^{\text{HVP}}_{\mu}$ in terms of each
other, is obtained. By making use of the derived relations the explicit
expression for the next-to-leading order spacelike kernel function, which
enters the representation for $a^{\text{HVP}}_{\mu}$ involving the hadronic
vacuum polarization function, is obtained. The corresponding next-to-leading
order spacelike kernel function, which appears in the representation for
$a^{\text{HVP}}_{\mu}$ involving the Adler function, is calculated numerically.
The obtained results can be employed in the assessments of the hadronic vacuum
polarization contribution to the muon anomalous magnetic moment in the
framework of the spacelike methods, such as lattice studies, MUonE project, and
others.
