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If you insist on using the built-in Android email client, you can periodically manually bulk move all of your local phone sent emails into your server-side sent mail folder. This is an Android problem and not a IMAP problem. This means that the sent folders of your phone and your server will not be in sync. It insists on using a local phone sent folder when sending email. You MAY be referring to a problem in some Android versions with the built-in email client where Android's email client will not allow you to use a server-side sent folder as the folder used to store sent email from the phone.
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It works for received and sent emails as well as anything else on the server, including folders of stored or archived emails. You are incorrect that IMAP only works for received emails.
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