  This addendum provides results complementary to those obtained in [J. Phys.
G49, 055001 (2022)]. Specifically, an equivalent form of the relation, which
binds together the "spacelike" kernel functions for the hadronic vacuum
polarization contribution to the muon anomalous magnetic moment
$a^{\text{HVP}}_{\mu}$, is obtained. It is shown that the infrared limiting
value of the "spacelike" and "timelike" kernel functions, which enter the
representations for $a^{\text{HVP}}_{\mu}$ involving the Adler function and the
$R$-ratio, is identical to the corresponding QED contribution to the muon
anomalous magnetic moment of the preceding order in the electromagnetic
coupling. The next-to-leading order contributions $a^{\text{HVP}(3b)}_{\mu}$
(which includes the leptonic and hadronic insertions) and
$a^{\text{HVP}(3c)}_{\mu}$ (which includes the double hadronic insertion), are
studied. The three kernel functions appearing in the representations for
$a^{\text{HVP}(3b)}_{\mu}$, which involve the hadronic vacuum polarization
function, Adler function, and the $R$-ratio, are presented for the cases of the
electron and $\tau$-lepton loop insertions.
