Can I export my email, contacts, or calendars?
Absolutely. You can export an MBOX file with all your email and attachments any time. You can import that file into Apple Mail, Gmail, Outlook, and other services. You can also export all your contacts into a single vCard. You can export your calendar data as .ics files.
To export your data, head over to app.hey.com/accounts in a desktop browser and click the Export Your Data option. HEY will send you an email when your data is ready to download: