The most important thing while transferring the server is to transfer the web sites including database, emails, email forwarders etc. If you do it manually then it takes long time to migrate the web sites from one web hosting account to another. cPanel/WHM has a feature to transfer the web site from one server to another. There are many options available as follow:
[1] Copy an account from another server. [You would require root password of the old server]
[2] Copy an account from another server with account password.
[3] Copy multiple accounts/packages from another server.
Based on your requirements you can select the option to transfer the web sites.
If you have any questions related to cPanel/WHM, just ask your questions in our webmaster forum.
Kailash Aghera