Some email programs, such as Microsoft Outlook (client), include a spelling checker. Outlook Web App relies on your web browser for checking spelling. That’s why you don’t see a spellcheck button or spelling settings in Outlook Web App.
Spell checking is available in Internet Explorer 10 and later versions, and current versions of Firefox, Chrome, and Safari.
Check the options for your web browser to learn more about how to use it to check spelling.
To learn more about the browsers that are compatible with Outlook Web App, see Supported browsers for Outlook Web App.
There are also add-ons for Firefox, which I suggest you try and get back to us here with your findings. So far, none were particularly highly ranked, but I assume with 3 starts out of 5 they are still worth trying out.