Gmail puts emails sent via SMTP in sent folder automatically.
On other servers it depends and unfortunately there is no extension that allows to check that.
You can use IMAP and UploadMessage to upload message to sent folder after sending:
using (Imap imap = new Imap())
{
imap.Connect("imap.server.com"); // or ConnectSSL for SSL
imap.UseBestLogin("user", "password");
FolderInfo sent = new CommonFolders(imap.GetFolders()).Sent;
imap.UploadMessage(sent, email);
imap.Close();
}
You can find entire sample here:
https://www.limilabs.com/blog/upload-email-to-sent-folder-after-sending