Firm Gmail, i.e. Google Apps -email, with K9 -email program?
The default settings by K9 have at least two mistakes:


  
  use imap.gmail.com instead of mail.gmail.com.
  use full emails for usernames such as forname.surname@myFirm.com, not just forname.surname.
  


Example settings


  Incoming Email settings
  
  
    Username: forname.surname@myFirm.com
    
    Password: correct
    
    IMAP server: imap.gmail.com
    
    Security type: SSL (always)
    
    Port: 993
    
    Use compression on network: Mobile Wi-Fi Other
  
  
  Outgoing Email settings
  
  
    Outgoing Server Name: smtp.gmail.com
    
    Use Authentication: Yes
    
    Use STARTTLS: Yes (some clients call this SSL)
    
    Outgoing Server Port: 465 or 587
    
    Username: forname.surname@myFirm.com
  


Some useful information extracted from this blog here.