Since this person has migrated from DreamHost to gmail, and is now upset that his old man is “gone”, you said that his old mail will still be on the dreamhost servers, which is true.
In his new GMail accounts, he can go to:
Settings -> Accounts -> Get Mail from Another Account
Once he puts in his OLD DREAMHOST account info, like you suggested, IE) Finding his old mail server, then putting the old mailserver in as the POP address, and his old user name and old (dreamhost) password into the fields. Google will then POP his old mailbox, and “import” all of his old mail from the DreamHost mail server, and it will just be in his new account.
At that time, (after all of the email has been migrated) I would then just delete the old dreamhost accounts. Also, if you delete the old dreamhost accounts, and after all of the mail has been migrated. You would want to delete that account from the google account. No point in having it attempting to check an empty mailbox, or a mailbox that you’ve deleted.
If he ever leaves gmail, and setups a new account somewhere else. I would do the same thing, except you would POP to the gmail account, and then you never have to lose email.
In fact, I still have email from 1994 in my gmail account.
I hope this explains it.