To fix this error I did the exact opposite of what that website says.
What happens is that MySQL had the password stored in the old format, change the password to the new format.
To check this, open the MySQL console (mysql.exe in Windows) and run:
SELECT Host, User, Password FROM mysql.user;
If the Password column is a 16-digit hexadecimal number, then the password is in the old format.
Then you have to execute:
SET PASSWORD FOR 'your_user'@'your_host' = PASSWORD ( 'your_old_password');
Where your_user is the user name and your_host is the hostname as appear in the corresponding columns and your_old_password' is the old password stored without encription (plain text).
That solved my problem.
Regards.