What is the Sharia ruling on a breastfeeding woman postponing making up for missed Ramadan fasts if she fears for herself or her baby, and is it permissible for her to postpone it until after the next Ramadan?

There is no harm for a pregnant or breastfeeding woman to break her fast in Ramadan, and it is obligatory for them to do so if they fear perishing or severe harm to themselves or their children. It is permissible if they fear illness or its increase.

They must make up the missed fasts before the next Ramadan. If they are unable to make up the fasts due to a valid excuse, then there is no expiation (fidyah) upon them. If they delay making up the fasts without a valid excuse until the next Ramadan begins, then both making up the fasts and expiation become obligatory upon them.