Sorry you have had to wait for a response!
Basically, your emails are stored either locally on your machine (Laptop, Tower, Tablet, Phone) or in your mailbox in the cloud with your ISP. That may be Google, TalkTalk, BT, Sky etc
All you need to do is move them to a local folder and archive and back them up to a storage device of your choice. So in your email client, and you are using two of the worst imagineable, create local folders and drag and drop from your ISP mailbox to your local machine.
Your biggest problem however is that whilst you may archive these e-mails in the native formats that each of those programs use, they are not directly compatible with each other. By that I mean you cannot simply import the formats into the other email client.
Lets face it, Windows Mail ceased support a few years ago - why are you still using it? LOL