Can I migrate mailboxes from Office 365 tenant to another Office 365 tenant?

Hi,

Yes, use a a third-party tool. It is the fastest and easiest way for you to migrate mailboxes between two tenants. If you are changing domain at the same time these tools can help you rewriting addresses in your mail objects. Some tools also help you to create the new users in the new tenant and assign licenses.

You could export mails to PST and import them but will take you a while and will be more complex so the time you have to put on it will be more expensive than the license cost for the third party tool.