Apart from paying £2k a year for a tool like ShareGate, what is the easiest way to copy content from one tenant to another?
For moving the entire lists, I suggest you save them as templates. List templates can be downloaded locally and uploaded to other sites. For reference you can refer – https://community.office365.com/en-us/f/148/t/355418.
Alternatively, you can ask me, if you face any problem in moving content from one talent to another.
