Hi Edward Stewart,
As far as I know, Outlook does support opening eml-files and it doesn’t offer a way to import them into Outlook.
You can check the information in
this article which contains instructions and 2 scripts to import eml-files into an Outlook folder.
(Please Note: Since the web site is not hosted by Microsoft, the link may change without notice. Microsoft does not guarantee the accuracy of this information.)
Besides, What's your account type? For Exchange or outlook.com account, items are saved on the server. You can configure your account in Outlook. Emails will be downloaded to Outlook client from server automatically.
Hope the information is helpful to you.
Regards,
Perry
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