Thank you for your post.
Create a script with the following commands:
Set Variable [ $File ; Value: Get (DocumentsPath) & <filename.fp7> ]
Send Mail [ Send via E-mail Client; No dialog ; To: <email address> ; (Subject and Message optional) ; $File ]
In FileMaker Go, the database file is stored in the DocumentsPath. Therefore, the first line creates a variable ($File) that contains the database file in the DocumentsPath. In the second step, an email is created that attaches the database file. The mail application will display, and you must tap "Send".
Let me know if you need additional clarification.
I think the key question here is how to automate this on the receiving end. I think you'll hit a problem with trying to set up the system to automatically receive and download emailed attachments. This could even be very hazardous to system security as you wouldn't want your system to open/download just any emailed attachment as that could download one type of Malware or another into your system.
Once you have safely downloaded the attachment, a script could periodically check for the presence of such a file, import the data and then either close and delete or (better practice) move the file to another directory for archival purposes. A file manipulation plug in (Several are offered by third parties) would be needed to make this work.