Move websites (incl. imap en mysql) across webspaces

[DominickV]

Hi,

We offer both hosting and web design services,
Our cms usses dns to look up the appropriate website so for the cms to work the specific domainname has to link to the path of the cms.
The matter now is, a client of us who is using our hosting service decided he also wants us to create his website,

So we need to move his website from webspace 'hosting-client' to webspace 'cms',
But I couldn't find how to do this, the data like mysql and imap mail has to stay intact.

Anyone any suggestions?