SQL Server 2008 Express backup and restore to test
Full Backup always constitutes of (.mdf) and (.ldf) files as a whole DB inside Backup.If 200GB (.ldf) is the problem, then as Raz Said, Switching the recovery model to 'SIMPLE'. Follow this; Take full backup if possible before switching [if free disk space is present].
Change the recovery model to 'SIMPLE' and click OK. then again revert to 'FULL' model. Shrink the (.LDF) file now it should be able to see the (.LDF) size reduced to few MBs. Now take Full Backup and move it to 2012 server.