You don't say whether you have the Briefcase in removable media, such as a USB flash drive, or if you update it over a network connection directly from laptop to server.
You do have to create a new Briefcase and drag the files you need to "sync" from the server into it. However, if you are networked, any files you have updated since the server was replaced could be transferred over the network connection first and then the updated files dragged into the Briefcase.
I have used Briefcases for several years to keep files synchronised between PCs in my home network, but was recently told about an application called "Allway Sync" - click here - which I have found to be very much better. It's certainly worth a look.