Hi Cloud Sellers!
Microsoft has released a native Outlook Web App client for iPhone and iPad devices. The client is available for download from the iTunes store: OWA for iPhone and OWA for iPad.
There is an excellent blog post and FAQ on the Office 365 technology blog here covering the solution.
Do note that a subscription to Office 365 is required and your tenant needs to be on the most current updates of the Office 365 infrastructure. You can verify which one your tenant is on by reviewing information here - Am I using Office 365 after the service upgrade?
Thanks! And good selling!