  We present the third paper about our ongoing HST survey for the search for
multiple stellar populations (MPs) within Magellanic Cloud clusters. We report
here the analysis of NGC 419, a $\sim 1.5$ Gyr old, massive ($\gtrsim 2 \times
10^5 \, {\rm M_{\odot}}$) star cluster in the Small Magellanic Cloud (SMC). By
comparing our photometric data with stellar isochrones, we set a limit on
[N/Fe] enhancement of $\lesssim$+0.5 dex and hence we find that no MPs are
detected in this cluster. This is surprising because, in the first two papers
of this series, we found evidence for MPs in 4 other SMC clusters (NGC 121;
Lindsay 1, NGC 339, NGC 416), aged from 6 Gyr up to $\sim 10-11$ Gyr. This
finding raises the question whether age could play a major role in the MPs
phenomenon. Additionally, our results appear to exclude mass or environment as
the only key factors regulating the existence of a chemical enrichment, since
all clusters studied so far in this survey are equally massive ($\sim 1-2
\times 10^5 \, {\rm M_{\odot}}$) and no particular patterns are found when
looking at their spatial distribution in the SMC.
