1. Choose Mailbox->Export Mailbox, or choose Export Mailbox from the Action pop-up menu (looks like a gear) at the bottom of the sidebar.
2. Choose a folder or create a new folder where you want to store the exported mailbox.
Outlook for Mac:
3. Choose File->Import Mailboxes. Select the mail application you want to import messages from.
If your mail account is configured on both systems as an IMAP account since the mail is on the server, both devices would see the same mail.
That doesn’t apply to your Outlook Contacts or presumably apple Contacts
This is a third party tool that transfers apple mail emails to windows outlook, converting them to .pst format, conserving the folder hierarchy and all the contents and attachments if any in the emails.
Both email client is supported by different OS Machine so manual or direct conversion of it is not probable third party tool is only the solution which can make it very simple and perfect.
The PCVARE MBOX to PST Converter is helpful for doing this task. I recently used it in my office for Apple Mail to Outlook. Export all Apple Mail or Mac Mail emails by export messages option then move all emails in Window OS and use the Tool to convert MBOX to PST Converter that is reliable solution and you can also try it for getting trust about its conversion.
One can convert .mbox files to PST file which is accepted by MAC as well as Windows Outlook editions. To do the conversion, a reliable software is required. You cab use QuickData MBOX to PST Converter which is available free of cost for trial purpose.