Post-asymptotic giant branch (post-AGB) stars are exquisite tracers of s-process nucleosynthesis, preserving the surface chemical signatures of their AGB evolution. The increasing chemical diversity observed among them challenges current nucleosynthesis models and motivates detailed case studies. In this study, we present a comprehensive abundance analysis of J003643.94
$-$723722.1 (J003643), a single post-AGB star in the Small Magellanic Cloud (SMC). High-resolution UVES/VLT spectra analysed with E-iSpec reveal a C/O ratio of 16.21 and an
$\textrm{[s/Fe]}$ = 2.09
$\pm$0.20 dex. In this study, we also report the first direct detection of lead in a post-AGB star via the Pb II 5 608.853 Å line, with a derived
$\textrm{[Pb/Fe]}$ = 3.18 dex. Comparison with a comprehensive and appropriate sample of post-AGB stars across the Galaxy, Large Magellanic Cloud (LMC) and SMC shows that J003643 has a relatively high C/O ratio, far exceeding the typical range of
$\sim$1–3. J003643’s
$\textrm{[C/Fe]}$ (1.33
$\pm$0.14 dex) and
$\textrm{[s/Fe]}$ (2.09
$\pm$0.20 dex) are consistent with expectations from standard third dredge-up (TDU) enrichment. However, its
$\textrm{[O/Fe]}$ (-0.08
$\pm$0.20 dex) is significantly lower than that of the comparative sample with similar
$\textrm{[C/Fe]}$ and
$\textrm{[Fe/H]}$, which typically show
$\textrm{[O/Fe]}$ between 0.5 and 1.0 dex. This relatively low
$\textrm{[O/Fe]}$, along with an [
$\alpha$/Fe]
$\,\approx0$ dex of J003643, is consistent with the chemical evolution of the SMC at
$\textrm{[Fe/H]}\,\approx-1$ dex, in contrast to the oxygen-enhanced Galactic and LMC trend at
$\textrm{[Fe/H]}\,\approx-1$ dex. This indicates that J003643’s high C/O ratio primarily results from its intrinsic oxygen deficiency rather than from an unusually high carbon enhancement. To better understand the CNO, alpha, Fe-peak, and heavy element nucleosynthesis, we compared J003643’s abundance pattern with yields from three stellar evolutionary codes: ATON, MONASH, and FRUITY, the latter two incorporating post-processing nucleosynthesis. While these models reproduce the majority of elemental abundances, they significantly underpredict the Pb abundance, highlighting a persistent gap in our understanding of heavy element production in AGB stars. J003643 represents the second s-process enriched single post-AGB star known in the SMC, stressing the need for more such observations. Its photospheric chemistry reflects the growing chemical diversity among post-AGB stars and reinforces the complexity of AGB nucleosynthesis beyond current theoretical models.