No, no, no and no.
a) Nobody ever observed a lasting memory in water. If you look at david4dev's answer above, with the shining formula, you have to be aware, that the timespan is orders of magnitudes too small, to be the reason for anything related with medicine. And it was not known to funders of homeopathy. It can't be the source of the theory, and it can't be the cause for some observation.
b) Water has no brain. What we know, to have a memory you have to have a brain. The metaphor of a brain might be too far stretched, but mechanical memory doesn't explain anything, too. david4dev's answer shows the possibility of deducting a molecule for a very short timespan. But it doesn't show, that there is a mechanism in the human body to deduct the substance - not even if there was much more time - for example: hours.
c) Even if there was a brain in water, what would that help? I can remember an antibiotic, but that doesn't give me the effect of an antibiotic. How should it work with water? It's not an explanation. You have to think it doesn't make a difference, if something is present or if you can detect that something has been present. You can detect, that a picture has been hang on a wall for a long time, and has been removed. But that doesn't give you the picture. The whole argument is a straw man, and isn't really related to what homeopaths have claimed. There is only an associative relation via different usage of the word 'memory', and failing to understand that, should be the exclusive joy of these esoterics, it is pseudo sceptic.
d) Historically, water drops from the clouds, runs through grass and earth, runs into small and bigger rivers and lakes, later into the sea, where it is shaken and shaken, tide goes up, tide goes down :) - and intermixed with all that other water, since millions of years, and should have all information by that way already. If this would work. But of course it's nonsense.