If your using Outlook you can select the "Leave message on the server until I delete it" so you would see all the same messages on all devices, both sent and recieved until you delete it via one of these devices.
This is by no means ideal, but achieves what I think you want to do. Obviously the other way is to just use a webmail client but it won't offer the "richness" that you have requested from the e-mail solution that you want to use
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