How do I switch my account from Outlook to Office 365?

It’s something absolutely possible and here is how to proceed:

Go to your Evercontact for Outlook Personal Page:

Click on the "Change to" tab. Don’t click anything yet.

Uninstall the Evercontact for Outlook add-in via the Windows Control panel:

Go back to your personal page and then click the "Switch to Evercontact for Office 365" button.

Then click "It's uninstalled!" in the pop-up on your Personal Page:

Give Evercontact authorization to securely access your Office 365 account by clicking "Continue" :

Click "Continue" to give Evercontact the necessary permissions, and then (if prompted) sign into the email account you want to switch to Office 365.

You're account will then be switched to Office 365, and you will be taken to your Evercontact for Office 365 dashboard for the first time.