We want to move a domain from Tenant A to Tenant B. We were told that we have to manually export emails from Tenant A and import them into Tenant B (when it's ready), which is fine. This is fairly easy to do with Microsoft Outlook for Mac.
I just would like to double check if the emails will be available just on the computer where we did the import OR will they be actually imported into the cloud and be accessible via Outlook.com as well?
When the emails are imported into Outlook, they will be synced up to Exchange Online and available via Outlook on the web. It can take a while for this to happen however based on the data size. While this method technically works, keep in mind there are some downfalls. This will take a large toll on your network bandwith depending on how many imports you try to do at once. I would at least consider doing a mass PST upload directly using Exchange Online: https://support.office.com/en-us/article/use-network-upload-to-import-your-organization-s-pst-files-.... Furthermore, there are lots of third party migration tools that specialize in Tenant to Tenant migrations that could improve your experience and cover other workloads, such as BitTitan and Quadrotech.