Have you checked the output from this script? From your description I
would expect this command to fail:

  EXEC sp_grantdbaccess 'USERB'

There is already a USERB in the database per your description. The
database user is part of the database, so it was included when you copied
the database.

What you need to do is to connect the existing database user USERB
with the newly created login USERB. (The logins are stored in master,
so the login USERB was not included in the copy operation.) You can
do this with the command:

  ALTER USER USERB WITH LOGIN = USERB

If this gives you a syntax error, it is because you have not applied SP2
of SQL 2005, which you should do.

There is one more thing you need to be aware of: in SQL 2005, passwords
are always case-sensitive. So if the script says:

 exec sp_addlogin 'USERB', 'TopSecret', 'MyDatabase'

and you try to log in with "topsecret" that will fail.

Finally, while the above commands work on SQL 2005, SQL 2005 now has
proper commands to create logins and user, CREATE LOGIN and CREATE USER.
There are no commands for adding users to roles though.