Mozilla is just a browser so he is simply browsing the files while stored on his mail hosts' servers.
Outlook express is NOT a browser and is not looking at the files on the mail hosts' server; it actually downloads the files from the pop server to his harddrive and then deletes them from the mail hosts' pop server.
Once they are downloaded and deleted from the POP server he will no longer see them in his browser because they are no longer on his mail hosts' server.
If he doesn't want it deleted from the online server then he could start using the Mozilla browser on the XP machine.
...Or...
He can open up outlook express and go to Tools ... Accounts. Choose the Mail tab and he should see his ISP mail host listed there ... select it with the mouse and choose Properties. Choose the Advanced Tab. At the bottom is an option ... Check "Leave a copy of messages on server". Note that now the only way they ever get deleted from the server is if he deletes them from within Mozilla. Also it may keep downloading a copy every time he connects with outlook express, even if he already read them (I'm not positive on this, it's possible it keeps a record of mail that was downloaded and doesn't download it again).
Frankly I find using web-based mail AND mail stored on your harddrive very confusing. I prefer harddrive based mail but I only have one computer. If I had multiple computers I might use web-based mail on both machines so it wasn't confusing and they both would always look the same.
BTW: as his email is set up there is no communication from one computer to the other about email via wi-fi. Both of them get their information directly from the mail hosts' internet mail server.
W7 doesn't have Outlook Express because Microsoft has retired it; if he ever upgrades his XP machine to W7 then his days of using Outlook Express are over.