We present some remarks about the embedding of spaces of Schwartz distributions into spaces of Colombeau generalized functions. Following ideas of M. Nedeljkov et al., we recall how a good choice of compactly supported mollifiers allows to perform globally the embedding of $\mathcal D'(\Omega)$ into $\mathcal G(\Omega)$. We show that this embedding is equal to the one obtained with local and sheaf arguments by M. Grosser et al., this giving various equivalent techniques to embed $\mathcal D'(\Omega)$ into $\mathcal G(\Omega)$.