Using classic Outlook for Windows in business environments
Dear Andrew Smith,
Thank you for posting in the Microsoft Community.
I understand your need to back up files in Outlook, and I'm more than happy to help. I noticed that you've chosen the classic version of Outlook, and I will provide instructions based on this version.
According to your description, you mentioned that the emails on the web version of bt mail have disappeared, but you can still see these emails in Outlook. So I infer that you connected this account using the POP protocol.
If you need to back up these emails in Outlook, please refer to the detailed steps in this link:
Export emails, contacts, and calendar items to Outlook using a .pst file - Microsoft Support
Regarding your second question, the emails shown in the Outlook on your laptop are different from those on your mobile phone, which is also related to the protocol you configured. For an account using the POP protocol, after the emails are received from the server and synchronized to the Outlook on your laptop, any changes made to these emails in Outlook will not be synchronized back to the server. In simple terms, the content of an account under the POP protocol only changes on the current device, and other devices will not synchronize these changes. So what you're experiencing is a normal situation.
If you need to have the same email content displayed, you need to configure bt mail as an IMAP protocol type in the Outlook on your laptop. This will enable two-way synchronization of the email content with the server. However, as a friendly reminder, if you configure it as the IMAP protocol and encounter the situation where emails disappear from the web version of bt mail again, these emails will also disappear in Outlook after synchronization.
I hope my explanations can provide you with some references. Feel free to post back if you need further assistance. Wish you have a good day!
Best Regards,
Ulrica.W - MSFT | Microsoft Community Support Specialist