The script below which you can run via SQL Server Management Studio (once per old/new server combo), that will transfer the configuration from one "old server" to one "new server", and update the scanserver value for existing related assets. You will need to modify the NewServer values with the NetBIOS name of your new server and OldServer with the NetBIOS name of your old server (name as shown in the web console).
Also, just to be safe, it's probably best to make sure you have a recent database backup.
Use Lansweeperdb
/* deletes the empty record of the new server, replace NewServer with the NetBIOS name of your new server (as seen in the web console) */
delete from tsysasservers where servername = 'NewServer'
GO
/* Renames your old server to the name of your new server, effectively transferring configuration. Replace NewServer with the NetBIOS name of your new server and OldServer with the NetBIOS name of your old server (as seen in the web console) */
update tsysasservers set servername = 'NewServer' where servername = 'OldServer'
GO
/* Moves the assets scanned by the old server to the new server, replace NewServer with the NetBIOS name of your new server and OldServer with the NetBIOS name of your old server (as seen in the web console) */
update tblassets set scanserver = 'NewServer' where scanserver = 'OldServer'
GO