OK, you are going to need access to the other account, so you can download the content/database etc. Depending on the size of the content and the speed of your Internet connection, it may be faster to use something like wget to directly transfer things between the old and new accounts.
As for the domain name itself, if this is not registered in your client's name, then you will need to transfer that. Also, there are some restrictions concerning moving domains from one DreamHost account to another, so you will probably need to contact DreamHost support and have them transfer the hosting for the domain between accounts.
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