How do I move multiple emails from one account to another one.

I have an email accounting expiring in a months time. But I have like around 6000 emails in it. Is there any available tools or ways to move it all at once or at least like 500 a time. I don't feel like doing it 1 at a time. I need it to be separate emails too. I don't want them all to be an attachment to a email as could be done from outlook.

Thanks in advance
suvi

 

outlook is the only way i know of,

 

Thanks sammie!
I found an archive functionality which is supposed to generate a zip file (as per the email provider) which I can use offline in outlook express. I am trying to generate it, but got server error 2 times so far on one of my biggest set of mails which are around 2000 in number. I got a couple of smaller sets of emails already. Let me try the other one one more time.

 

maybe it has a size limit try and split it in 2