A couple of hours of googling produced various results: she may loose an access to her email on migrating while others say that, for a limited period, she will be able to read the mail but not send, etc.
What you read is true for some ISPs, but not Tiscali. They keep your email account for ever, even if you don't access it. I've had one for over 10 years (a lineone.co.uk) which I haven't looked at for ages; just tried today, it's still there albeit empty.
What she does is use Tiscali's POP3 (pop.tiscali.co.uk) to read her mail from her Tiscali a/c, but her own ISP's SMTP to send mail (within the same email client, e.g. OE, Account).
I'm just wondering if there is an 'easy' but fail proof way of saving / transferring her emails.
Do you mean her actual emails? Has she just left them on Tiscali's server? She shoulda downloaded them to her PC using POP3 and then she would always have them saved, now and forever.