Response tells you the server's working. It's the login that's failing. You need to set a password for user alex, using
passwd alex
If you did that and login still fails, try looking at the PAM module's recent activities using
tail -n 100 /var/log/auth.log
You should see something like "Accepted password for alex" (for auth success) or "Refused user alex for service proftpd" (for auth failure). If you don't find any entries at all for user alex in auth.log, please post your proftpd config files, as password-authentication access may not be properly configured. If you do see PAM entries for alex, try checking your proftpd log for more information on the problem.
You didn't ask about security, but please be aware that FTP is inherently insecure. Proftpd also supports SFTP, which would give you much better security. I recently posted example proftpd config for supporting both password and ssh-key sign-in for SFTP here.