How to Sync iMac Mailboxes With an iPhoneby Bennett Gavrish
Although you can add and manage email accounts directly from an iPhone, some users may prefer to synchronize their email settings and mailboxes from their computer. For example, if you use the Apple Mail application on an iMac, you can use iTunes to transfer your email account settings to your iPhone. Then when you use the Mail app on your phone, the device will automatically connect to your email accounts and download the contents of your mailboxes.
Connect your iPhone to your iMac using an iPhone USB cable.
Launch the iTunes application if it does not open automatically.
Click the name of your iPhone from the Devices list.
Go to the Info tab at the top of the iTunes window.
Check the box next to "Sync selected Mail accounts."
Check the boxes next to the accounts and mailboxes that you want to transfer to your iPhone.
Press the "Apply" button to save the settings and begin transferring the email data to your iPhone.