A work or school account and a Microsoft account are two different accounts. A work or school account is an account created by an organization’s administrator to enable a member of the organization to access Microsoft cloud services such as Microsoft Azure, Windows Intune, and Office 365.
A Work or School account can take the form of a user’s organizational email address and it is different from your Microsoft account. Your Microsoft account is the one that you use for personal services like Xbox Live, Outlook.com, Windows 8, and Windows Phone.
Subscribe to Office 365 for Business plans for this tenant. And then he creates accounts in this tenant. These accounts are called work/school accounts.
Microsoft account is an account related to Microsoft consumer services. The user signs up for this email him/herself. They can create a new account like Outlook.com or use an existing email address. So, all email accounts can be signed up as Microsoft accounts.
The error "Microsoft Account does not exist" usually means:
The person is logging in using an Alias. If the user renamed the affected email address into a new account, the original account would become an Alias. Thus, logging in using the original account will trigger the system to prompt the user to tell the user that it does not exist.
The solution is to log in using the new account. If a person did not access the account (WITH A BROWSER) within 365 days. The account will be deleted permanently.
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