What you need to do with Gmail is not delete them, but archive them.
You don't actually create a second copy, you just attach a specific label to the message. When you archive them, that removes them from the inbox, and keeps them from being deleted. You can attach multiple labels to the same message, as well - it is much handier than having just specific folders you can put a message in. For example, I have messages that come from a specific website that I want to keep labeled as being from that site, but occasionally want to sublabel them as Inspirational messages, Recipes, etc. I attach the labels I want to them, then hit the Archive button. You can access specific catagories through the list on the left, and find all the messages you have previously labeled and archived.
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You don't actually create a second copy, you just attach a specific label to the message. When you archive them, that removes them from the inbox, and keeps them from being deleted. You can attach multiple labels to the same message, as well - it is much handier than having just specific folders you can put a message in. For example, I have messages that come from a specific website that I want to keep labeled as being from that site, but occasionally want to sublabel them as Inspirational messages, Recipes, etc. I attach the labels I want to them, then hit the Archive button. You can access specific catagories through the list on the left, and find all the messages you have previously labeled and archived.