I am searching for the *.eml files.
I have system level access to the phone's filesystem.
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While the path may be a little different on Windows, you should look in the app's package directory, which will be under the DefApps user directory (\Data\Users\DefApps). The package name (on the desktop but I think also on the phone) is microsoft.windowscommunicationsapps_8wekyb3d8bbwe.
I found a small number of .EML files by looking under the LocalState subdirectory of the app's data directory, but the bulk of the messages may be stored in a binary database. I found a number of binary data files, some quite large, while exploring the app's data dir.
It'll probably be the DefaultUser user account, somewhere in the AppData folder there should be a WindowsApps folder.
This is all off the top of my head but that's where I would start.