Like quite a few other people in this page I experienced the error:
Microsoft.Exchange.MailboxReplicationService.ProxyService/OAuth‎' failed. Error details: Access is denied
In my case it turned out to be caused by the fact that the source tenant admin used insufficient credentials when acknowledging the creation of the migration enterprise application in his tenant.
It took some time to troubleshoot this and would have been easier with these two suggested changes to the process/documentation:
1. When opening the tenant application creation link and clicking accept there is no feedback whether the operation was successful or not. It just redirects to a standard Microsoft page. This means source tenant admin is unaware if the migration application was created in his tenant or not.
2. The https://docs.microsoft.com/en-us/microsoft-365/enterprise/cross-tenant-mailbox-migration?view=o365-worldwide#step-by-step-instructions-for-the-source-tenant-admin should include to check in the Azure AD portal that the enterprise application used by the migration has been created and that required permissions on MS Graph and Exchange Online have been assigned. Only steps to validate the creation of the organization relationship are listed in the check list.
Otherwise, seems to work well, thank you.