Saving outgoing email through SMTP in webmail's Sent folder?

Is it possible?
I only tested with Roundcube and sent messages from website are not stored in there.
(only those sent through webmail)

Not important but just curious, thanks.

Not currently possible from our side, but most email clients actually do this themselves by pushing the email back over the IMAP protocol and into the Sent folder.

Many thanks, well noted.