Move profile to OneDrive

I think this is a bad idea. I'd rather set up the account as an IMAP account on all devices. This will you you the exact same view to your mail regardless of which device you use. All mail is managed on the server.

It's a little more complicated; bottom line is I can't store much mail on the server whose domain I'm using, so IMAP is out, but I may be able to cobble up something that allows the existing server to forward all mail to an IMAP server. Having all archived mail on the device is much better for complex searches, I think, but I really don't have enough real-world IMAP experience yet to judge that.

You could forward all your messages to a decent email provider who offers IMAP with a useful amount of space. Good email providers will let you set up an "external" email address as an alias or similar.

Well, that gives me something to go on, but I doubt their "external" address will allow another provider's domain. Now I guess I start by Googling "decent email providers" :).

Well I can name the big four free ones that all do as Zemos said.

Google, Yahoo, Hotmail and GMX.

All will allow you to set up the collection of email from your existing mail account. Some will also let you use their servers to reply using that account. However it is not difficult to set Thunderbird's account settings to save emails sent from one SMTP server to the sent mail folder on another account.

So when you send mail from say Me@myDomain.com Thunderbird can save the mail to the sent folder of You@GMX.com and thus the sent mail synchronizes.

Thanks, Matt. I had spent some quality time in Google and Thunderbird Help, and was pleasantly surprised at what could be done, but unclear on the big picture. Your post kind of put the big picture together. Now it's just a matter of doing it.