You will want to read Send and receive email with Office 365 Outlook Email adapter - BizTalk Server - Receive email using a receive port where it mentions the promoted property are under OfficeMail, e.g. OfficeMail.HasAttachments
For the send it has the following property, but is unclear if it uses that for the Receive as well.
The OfficeMail.AttachedFiles property value is list of files with "|" as delimiter in between different files. For instance: "C:\Attachments\File1.pdf|C:\Attachments\File2.xml".
The is also a property on on the Payload Tab, which is Deliver MIME. Have you tried it with that setting?
See also Attachments in the Office 365 Outlook Email Adapter, which mentions that the filename is the Message Parts name.