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I would never store eggs in this manner, because the texture and flavour degradation will make them unpleasant to eat. However, to actually answer your question--and again, I urge you not to do this because stored and reheated eggs will taste like garbage--cooked eggs should keep for up to 72 hours in the refrigerator.
After hard boiling eggs, they should be stored in the refrigerator as well. According to the American Egg Board, hard boiled shelled eggs can last up to one week if they have been kept in the refrigerator. If hard boiled eggs are peeled, eat them the same day as when they are peeled.