It has been postulated that chromatin modifications can persist through mitosis and meiosis, thereby securing memory of transcriptional states. Whether these chromatin marks can self-propagate in progeny independently of relevant trans-acting factors is an important question in phenomena related to epigenesis. "Adaptive cellular memory" displayed by yeast cells offers a convenient system to address this question. The yeast GAL genes are slowly activated by Gal4 when cells are first exposed to galactose, but their progeny, grown in glucose media, exhibit a fast activation mode upon re-exposure to this sugar. This "galactose memory" persists for several generations and was recently proposed to involve chromatin modifications and perinuclear topology of the GAL genes cluster. Here, we perform a heterokaryon assay demonstrating that this memory does not have a chromatin basis but is maintained by cytoplasmic factor(s) produced upon previous galactose induction. We show that Gal3, the cytoplasmic rate-limiting factor that releases the Gal4 activator, is dispensable for preserving galactose memory. Instead, the important memory determinant is a close Gal3 homolog, the highly expressed Gal1 galactokinase, the residual activity of which preserves memory in progeny cells by rapidly turning on the Gal4 activator upon cells' re-exposure to galactose.