It's also important to choose the server right folder for uploading sent messages -- should be same as used by other apps and web mail.
- Please long press on the account -> options and folders -> folders.
- Give it 5-15 seconds to refresh.
- Find the server side Sent folder (may be called something else, e.g. Sent Messages, Sent Items, may be in your language and not English, etc.)
- Tap its name and choose "Sync as Sent".
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PS - support
support / at / aqua-mail / dot com.
This email address is listed in Google Play on the app's page.
It's also listed on the web site which has a whole "support" section.
And then we have this forum here.