I would hazard a guess (emphasise 'guess') that you may have a mismatch between the configured SMTP server for outgoing mail, and an IMAP server for incoming (syncing of mailboxes).
Or it may just be that the servers do match but password for SMTP is correct and IMAP is wrong, though I'd expect the client to report some connection errors if that were the case. One worthwhile step would to prove that incoming mail actually works, i.e. send an email to your friend, at the address she's using on the iPad etc, and confirm that she received it and can see it on the iPad?
The actual settings depend upon the mail provider but by way of example, a gmail account might use smtp.gmail.com for outgoing mail, and imap.gmail.com for incoming.
But I emphasise above is just a guess, or at best a hunch. And I am assuming you are using IMAP, that assumption may be wrong. Others may have better ideas.
