I built on top of Izzy's comment
Having your "Sent" folder defined on all your clients (and always having defined the same), you should be able to easily view your sent mails from all clients, regardless of the fact from which client a mail was sent.
It really means that every client -- I mean every -- such as Mutt in Server, Evolution in Desktop, K9 in Android, Online settings such as Gmail-labels/filters, iOS email more here, desktop settings such as here and here -- must have corresponding settings. If one part is missing, your IMAP mailbox won't work over multiple devices or it has limited capabilities.
I gather below some errrors that I had to fix in order for IMAP work over multiple devices.
'You have sent a message in a trashed conversation...' -- fix this error in Gmail, more
It may be because of filters or wrong setups.
Gmail folders are called
"Labels", make sure you have cross in a visibility -button, more
In mutt, make sure you have the record line correctly like this:
In iPad, make sure this here
again and make sure
Settings > Mail, Contacts, Calendars >
Your@Email.com > Account > Advanced > Sent corresponds to your other
settings -- not something like
In Desktop, make sure your Desktop client has right settings more here,
(Debian -biased questions).
Next time you may have the same problem with other folders such as
Deleted Messages -- yes I know -- it is irritating that different email-clients use inconsistent terminology so you need to adjust every name and delete all extra folders/labels later.
I hope you luck, my setup looks to work but I am still fighting with a minor issues such as removing extra directories in K9, anyone knowing a solution to that?