Can I send email unauthenticated to an internal SMTP server which then relays onto authenticated SMTP?

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http://serverfault.com – I have a back-end system which only supports sending email to an *UN*authenticated SMTP server, however, ultimately it needs to go via an authenticated SMTP server on the public internet. My idea was to send it internally to a local SMTP server unauthenticated, and then have that middleman server relay to an authenticated public SMTP server (such as gmail) with the relevant credentials. Can this be done, any recommended SMTP servers? By the way, searching on Google with search terms "unauthenticated" and "authenticated" in the same query doesn't seem to get me far, it just gives me a load o (HowTos)