You can use migration software or the native Microsoft method to ensure data integrity and minimize disruptions when transferring between Office 365 tenants. The native method is a logical process which cannot be done easily. MailsDaddy Exchange Server Suite provides smooth transitions, transferring emails, documents and settings in simple steps for data conversion and migration. Also, OST, PST, EDB etc. can also be recovered easily.
For more information read here - https://www.mailsdaddy.com/office-365-to-office-365-migration/
Read here for the free manual method to migrate Office 365 to Office 365.