Transferring from Windows mail

I have a client wanting to move to a new laptop (Win7/8). The problem is what to do with her emails. I've have had very mixed experiences with moving Windows Mail data (it's a mess and wasn't thought out too well by Microsoft in my opinion). I want to move her ideally to Hosted Exchange using Outlook. I'd be grateful for any ideas and advice how to meet her needs and not lose any emails. I suspect it'll involve moving it into Outlook then exporting to a .pst. And/or moving her to the Windows 8 Mail App.

BT Yahoo is a UK email service via Yahoo.

Below is the description I asked my client to describe in her own words:

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I use Windows Mail, a very old program. I started using it originally when I got my Dell in 2001, then I transferred it (either just the emails, or the program itself as well, can't rememeber) onto this current laptop (Dell XPS M1530, Windows Vista).

And now I'm about to buy another laptop and don't want to lose my past 13 years' worth of emails. I can't switch to using the emails saved on the server because a) they're not arranged in my folders and b) I've gone through and deleted loads of them at various points c) Windows Mail contains all my emails from a variety of different email addresses I've used over the years, including two different universities - none of those are saved in my BT Yahoo email account. I wouldn't mind continuing to use Windows Mail, but there may come a point where technology doesn't allow me to use that program on a new laptop any more, so I need to start thinking about what email program to switch to, and how to save all my old emails so I can still access them going forward.

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