If you want to keep myapp.dreamhosters.com, you can just set up hosting for theirdomain.com and either redirect or do a dreamhost-style mirror of myapp.dreamhosters.com.
If you don't want to keep myapp.dreamhosters.com, you can add hosting for theirdomain.com and point it to the web directory you already have for myapp.dreamhosters.com. You can then delete the domain myapp.dreamhosters.com.
Regarding DNS setup you can either use the current dns setup and point to IP of the appropriate dreamhost server or you can us the dreamhost nameservers and set up a custom MX record pointing back to your friend's mail server. The latter has the benefit of avoiding having to change the IP in the DNS record should DreamHost ever move you to a different IP address.
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