Emails sent with my Lumia do not appear in Yahoo! Mail

Emails sent from your Lumia are by default stored in a folder called 'sent items'. Navigate to the 'sent items' folder on your Lumia and if given the option select 'sync this folder'. You will find the same contents in Yahoo! mail under the folder Sent items which can be found from Folders > Sent items.

Similarly, if you want to ensure any emails sent from Yahoo! mail from within the web interface are synchronised with your Lumia, then perform the above operation on the folder 'Sent'.