The "correct" way to handle this is to not forward the mail at all. Instead, deliver it to the user's mailbox normally. The user then adds this "external accou

The "correct" way to handle this is to not forward the mail at all. Instead, deliver it to the user's mailbox normally. The user then adds this "external account/mailbox" in their Gmail settings and Google will automatically retrieve any mail from that mailbox (via POP3) and place it in their Gmail account.