Glycosylphosphatidylinositol-anchored proteins (GPI-APs) are anchored at the outer phospholipid layer of eukaryotic plasma membranes exclusively by a glycolipid. GPI-APs are not only released into extracellular compartments by lipolytic cleavage. In addition, certain GPI-APs with the glycosylphosphatidylinositol anchor including their fatty acids remaining coupled to the carboxy-terminus of their protein components are also detectable in body fluids, in response to certain stimuli, such as oxidative stress, radicals or high-fat diet. As a consequence, the fatty acid moieties of GPI-APs must be shielded from access of the aqueous environment by incorporation into membranes of extracellular vesicles or into micelle-like complexes together with (lyso)phospholipids and cholesterol. The GPI-APs released from somatic cells and tissues are transferred via those complexes or EVs to somatic as well as pluripotent stem cells with metabolic consequences, such as upregulation of glycogen and lipid synthesis. From these and additional findings, the following hypotheses are developed: i) Transfer of GPI-APs via EVs or micelle-like complexes leads to the induction of new phenotypes in the daughter cells or zygotes, which are presumably not restricted to metabolism. ii) The membrane topographies transferred by the concerted action of GPI-APs and interacting components are replicated by self-organization and self-templation and remain accessible to structural changes by environmental factors. iii) Transfer from mother cells and gametes to their daughter cells and zygotes, respectively, is not restricted to DNA and genes, but also encompasses non-genetic matter, such as GPI-APs and specific membrane constituents. iv) The intergenerational transfer of membrane matter between mammalian organisms is understood as an epigenetic mechanism for phenotypic plasticity, which does not rely on modifications of DNA and histones, but is regarded as molecular mechanism for the inheritance of acquired traits, such as complex metabolic diseases. v) The missing interest in research of non-genetic matter of inheritance, which may be interpreted in the sense of Darwin's "Gemmules" or Galton's "Stirps", should be addressed in future investigations of the philosophy of science and sociology of media.