Dispersing these oily solutions in aqueous PVA, to form Oil droplets, spontaneously yields W1/O/W2 single core double emulsions, with W1 enriched in the hydrophilic polymer initially dispersed in oil. We also report experiments at the scale of a single oil drop evidencing the diffusion of water, and show how the stability and rheology of the final double emulsions depend on the phase fractions and polymers concentrations. Additionally, we found that PNIPAM-COOH co-dispersed in oil with PEG, stabilized multiple core double emulsions when deprotonated (in basic PVA solution), which turned into single core double emulsions when pH was decreased.