Always use Outlook Desktop Application. It can work when you're offline with no Internet connection (same with desktop Excel, Word, PowerPoint, etc.)

If your computer is offline/not connected to Internet, Outlook on your desktop will not send or receive emails or calendar updates. You can  continue writing emails and press ‘Send’, the emails will be stored in your ‘Outbox’.

When you are connected to the Internet again, the emails and calendar updates will be sent from the Outbox automatically.

If you like, you can also download the Outlook App to your phone for on the go communication. Avoid logging in online from other persons computers as it can lead to a breach in security.