Deleteing emails as they are forwarded is up to you. You can have either an address that only forwards emails (and doesn't store them) (you can have an unlimited number of these) or you can have an address that stores them AND forwards them.
Intuitive? It aint gmail, but it is pretty straight forward. If it's a deal breaker for you, and you are willing to use me as a referall if you send up PM me and I will create a very temporary email account for you that you can test.
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