I am going to make a guess.

You are using POP not IMAP or Exchange or any thing like that.

There two items you are going to want to look at.

First - export and import. use the file > import export features. Its all wizardy and warm and friendly. Just read evrey screen and use logic and you will be able to move files easy.

Second, make sure that this doesn't happen again by going to TOOLS>Acounts>Mail tab>Prperties> advanced tab and then selecting both Leave copy of messages on server, and delete from server when deleted items are emptied.

this iwll allow you to view from euther machine without gettin a mail read gap going.

HOWEVER! If you are using POP then that tells me that you are outsourcing email, probaly to an ISP or a cheapo depot mail service. They Use POP becasue it keeps the traffic onthier servers lower, and it reduces thier storage burden. They will likely have placed a mailbox size limit in place, so you will have to start archiving files if that is the case.