Hi Christian,
In regard to the issue, currently it’s not available to automatically migrate mailboxes from a P Plan to an E Plan. You can create a .csv file to import users to Office 365, however a cutover migration is used for migration from on-premises server to Office 365, and it won’t be available when you migrating from an Exchange Online server to another Exchange Online server.
Another workaround here is that you can let your users to manually forward all the mails from old mailboxes to their new mailboxes, but they’ll still need to export the Calendar and Contact items from the old one to the new.
Please feel free to post your updates here at your convenient time.