Most email programs generally ERASE the email from the server, as soon as they are downloaded. This is the default setting. As a result, whichever PC happens to check first will grab any pending email and then tell your server to erase it.
However, this is a setting that can be changed on both machines.
Go into the ACCOUNT PROPERTIES for that particular email account. There will usually an ADVANCED SETTINGS area within, where you can set it to:
X LEAVE A COPY OF MESSAGES ON SERVER.
X REMOVE FROM SERVER AFTER ___ DAY(S). (3 days should do it)
This way, the computers will both be allowed get the same emails - as long as they both "check in" with the server, within 3 days of each other. The web/email server will keep all email for that period of time, so computers can retrieve it.
I hope this is helpful
Best regards,
Mike