I haven't tested this on different server versions.  In this instance, I moved DHCP from a Windows 2003 Server to another Windows 2003 Server.

I've seen at least one other method which involved some command line activity but this method seems simple enough.

On both the source and the destination server, launch the DHCP Manager, right click on the server name, select:

All Tasks
Stop

On the destination server, browse to:

C:\Windows\System32\DHCP

Delete the contents.

Browse to the same location on the source server and copy the contents from the source server to the destination server.

Go back to the DHCP manager on the destination server, select:

All Tasks
Start

Right click on the server name and select:

Authorize

If you refresh, you should now see the desired data and the DHCP server should be operational on the destination server.

You'll want to return to the source server and disable the DHCP in services to prevent it from starting in the future.