I don't think there's a trigger for when you send an email, but if you think outside the box a bit you could use When a new email arrives in a shared mailbox (V2) and point it to the Sent Items folder with a Subject Filter to only match the items you want. Note that I'm just using When a new email arrives as I don't have access to a Shared mailbox, but would be the same setup.
Then you can use Export email and Create file. See full flow below.
When a new email arrives uses the Sent items Folder with a Subject Filter.
Export file then exports the actual email so we can get the content.
I've then got a Compose to build up the filename I want to use when saving it to SharePoint. I'm using concat to combine the Subject and Received Date/Time. The reason I do this is to ensure we don't get files with the same name.
concat(triggerOutputs()?['body/subject'], ' - ', formatDateTime(triggerOutputs()?['body/receivedDateTime'], 'yyy-MM-dd-hhmmss'), '.msg')
Below is a sample of what the name might look like.
And finally Create file to save it in SharePoint.
