Sometimes migrating mailboxes from on-prem to Exchange Online is easy. But when it comes to moving mailboxes from a GoDaddy managed tenant, getting Admin access to perform the export is almost impossible. Here's one way that seems to work.

Export mailbox contents

1. Log into the Compliance Centre as an account admin (https://compliance.microsoft.com/)
2. Select eDiscovery | Core from the left blade
3. Create a case
4. Apply a search to the case.  From the menu bar, select Searches and then + New Search
   1. Select Specific locations, and then Exchange Mailboxes only
   1. In Define your search conditions select the date range for mailbox items
   1. Review the search and click Submit
5. Wait until the search you have just submitted completes
6. Initiate the export of mailbox items found in the search
   1. Click on the search you created in step 4 and details should be shown in the right-hand blade
   1. Click Actions | Export results
   1. In the Export results blade, leave defaults as they are (particularly Export Exchange content as One PST file for each mailbox
   1. Click Export
7. Download export results (must be done from Edge)
   1. Click on Exports in the menu bar
   1. Select the export that you have created in the previous step
   1. Wait until the export completes (this may take a few hours)

Update folder structure in PST files

The exported PST files will need to be modified so that they have a similar folder structure to the target mailbox. If you open the exported PST, you'll notice that the Inbox is in a subfolder under <mailbox name>(Primary store)/top of information store/. Simply locate the Inbox and move this to folder root. Repeat this for any other folders that need to come across. Delete any folders that don't need to come across (like the now empty <mailbox name>(Primary store)/top of information store/ folder).

To make these changes, open the PST in Outlook, made changes, then close the PST.

Note that if this step is not done, a new folder structure will be created in the target mailbox for the imported items, rather than them being merged with the target inbox.

Import mailbox contents

Follow these instructions in the new tenant: https://docs.microsoft.com/en-us/microsoft-365/compliance/use-network-upload-to-import-pst-files?view=o365-worldwide

First step is to create an import job

1. Again, log into the Compliance Centre as the account admin (https://compliance.microsoft.com/)
2. Select Information Governance | Import
   1. Note that PST files should be < 20Gb
3. Follow the instructions provided
4. Download and install AzCopy as per the instructions. Note that:
   1. If you get an error when trying to upload PSTs with AzCopy, then the SAS URL must be modified to enclose all & in double quotes (ie & becomes "&"). Alternatively, close entire parameter values in closed double quotes.
   2. You can use this spreadsheet as a template to create AzCopy commands
   3. Use the /NC2:2 switch on slower upload speeds to avoid timeout. Lowers thread count to 2. More here.
5. Check that AzCopy uploaded the correct number of PST files
6. Create a mapping file, using this as a template
   1. Note that the fields FilePath will usually be blank and the TargetRootFolder will usually be / (ie Inbox)
7. Select the mapping file and complete the import.

Next step is to run the import job to import into Office 365

1. Select the import job you want to import
2. Click on Import into Office 365
3. Select whether you would like any filters applied (ie only import items from the last 12 months)
4. Select OK to commence the import