The way Paubox solution works is by wrapping around domain names and rerouting the inbound and outbound email linked to that domain through our secure cloud based encrypted server. If you have a domain name, we can wrap around that and replicate existing emails tied to your domain or create new ones from scratch, i.e. Customer.Name@yourdomain.com
Office 365 - In the case where you are using Office 365, we actually integrate via connector without taking over email hosting. Microsoft would continue hosting your email and taking care of at-rest encryption, we would be taking care of the in-transit encryption in the background.
G Suite - For G Suite users, we integrate without taking over email hosting. Google will continue hosting your email and encrypting all emails at-rest and we will be taking care of encryption for all emails in-transit in the background. You can continue using the emails you have tied to your domain, i.e. example@ , and can continue accessing your email through gmail or any other email client, such as Outlook, MacMail, Thunderbird, etc.
Pauboxmail.com - Paubox also offers the solution of creating / hosting your email account within our pauboxmail.com domain. Customers often use this solution if they do not have a domain or decide not use their domain for handling encrypted email.