Backing up Outlook emails to OWA

We have a Small Business Plan on Office365 and we have successfully configured this.

Email is configured in Outlook 2013 on the PC, and works correctly.

What we want to do is for sent items from Outlook 2013 to appear in sent items in OWA in Office365. This doesn't do it at the moment, and not sure if it's even possible to do.

If not, what other alternatives can be done to allow for emails sent on the PC to be viewed online without having the PC to hand?

Thanks

Karl