Postbox contains an importer that will copy local messages from other email clients such as Apple Mail. However, sometimes the importer will skip messages that have message structures it doesn't recognize.
As messages are imported/exported over time, their structure can become corrupted, much like a game of telephone where the end message structure is different than the original. When Postbox encounters these messages, it can sometimes account for them, but when it can't the Postbox importer will skip them.
We recommend performing the following steps to help clean these message structures:
1) Within your old email client, choose an existing IMAP account, or create a new IMAP account such as Gmail for the purposes of transferring messages.
2) Drag the folders from your local account to to the IMAP account. This can help to "clean" the messages as the are transmitted from the client to the server.
3) When complete, install Postbox but do not import messages. Rather, setup your accounts in Postbox, and then you have the choice between keeping the messages on the IMAP account or copying them to your local account.
We never recommend keeping messages on your local account. Keeping messages on the server is a great way to backup messages should your computer be lost, stolen, or damaged.