Some email programs will show the date you imported the converted mail as the date for each message in the message list. This is usually incorrect behavior of the new email application because it is trying to find a “received” date and not finding one.
To fix this, change the displayed columns in your email program to show “sent” date instead of the “received” date. The sent date is the real date of an email message per the RFC-2822 specification. There is no specification for received dates and every application interprets the idea differently.