To migrate mailboxes from one tenant to another in Microsoft 365, you need to perform Office 365 Tenant to Tenant Migration. It can be done manually or with migration tools or services. Manual process is very lengthy and complex also.
For complete process, read this article on Tenant to Tenant Migration. It will guide you step by step in completing the migration.
Also read about Google Workspace to Office 365 Migration and Best OST to PST Converter