I currently receive my email through Cox Cable, then into Windows Live Mail.  Within WLM I have many storage folders with saved emails.  I have re-created these same folders in my Cox webmail account.  I need help on how I can move, save, or import these saved messages in WLM into my Cox email.  I tried forwarding them to my Cox email, some showed up on the server email, others did not.  I also worked with Dell tech support and tried to import them to a Mozilla Thunderbird email account, they imported with the storage folder name, but all the messages inside the folders were corrupted.

I'm planning to buy a new computer and switch to Windows 10, but would like to save these messages on my Cox webmail so I have them out there to transfer to my new computer's  Windows 10 mail.

Anyone, please help how I might accomplish this.  There are several hundred emails that I want to save and transfer.

thanks, SoonerSlim