Normal Office 365 accounts would only have a 50gb mailbox, any more then this and I would recommend enabling Archiving which can go to 1TB
- Add Trial verison of a license with Exchange Online Plan 2 which increases their Mailbox size to 100GB ( e.g.M365 E5 ) for a month for Migration. Assign this to the user to get their Mailbox size to 100GB
- Migrate the email with Bit-Titan can do a prestage and only do items old then a couuple of years to start with,
- Wait for the Sync, if you synced over 100gb it will come up with a failure
- Enable Archive on the 365 Mailbox. Archiving runs every day , you can force start with this
- If the source mailbox is below 100GB you can enable archiving to drop it back down to 50gb then remove the license.
- If the source mailbox is over 100GB , let the Archiving finish , then rerun the Sync until its completed ( It will make a note in the database of items its already replicated )