Anything in the 6.7 branch can be migrated to 7; you'll want to go ahead and upgrade to the current 6.7 branch (6.7.3) then migrate it to the new server, THEN preform the migration there (should you want to actually migrtate using the install files)
What I'd do would be:
On CURRENT server
1. Backup your CGI and VARS directories
2. Backup your Members and Non-CGI directories.
3. Migrate them to the new server, edit vars_config.cgi to reflect "new paths" and the url of the new server.
4. Check the CHMod's on files to ensure they'll run (755 on non vars files, 666 on members files, 666 on vars files IIRC)
--- MAKE SURE .C is running on the "new server" before moving on. ---
5. follow my "migrating from UBB.C6 -> UBB.T7" guide.