I have recently gone through an informative article that explains the detailed manual and a professional solution to perform Office 365 tenant to tenant migration. This article defines the prerequisites that you need to perform before initiating the manual procedure. Apart from this, you will find reliable resources that explain the detailed manual procedure to accomplish the cross-tenant migration for Office 365. 

The manual method is quite complicated and requires technical knowledge of the entire Microsoft 365 admin panel. It leads to a high risk of data loss. Thus, experts have always recommended opting for a professional software solution that includes a secure Office 365 migration tool. This utility offers some additional features that will allow you to optimize the whole migration process. Apart from this, you can also try its free version to analyze and experience its advanced functionalities.