Forum Discussion
Migration G Suite for Office 365
There are 3rd party tools but why not check out FastTrack for Office 365 first, which I think you might qualify for, though do double check the eligibility. This is a no-cost option for qualifying organizations, where Microsoft offers a migration service:
"Mail can be moved to Exchange Online from on-premises Exchange Server, IBM Domino, Google Apps for Work, Novell GroupWise, or IMAP-capable systems. Files can be moved to OneDrive for Business from Google Drive, Box, or file shares and to SharePoint Online team sites from file shares. OneDrive for Business migration from a single G Suite environment (Google Drive only)."
https://fasttrack.microsoft.com/office?offers=1
https://technet.microsoft.com/library/dn783224.aspx?f=255&MSPPError=-2147217396
https://technet.microsoft.com/en-gb/library/mt651702.aspx
Also, there is a new offer that might be worth checking out (for new OneDrive/Office 365 customers only):
https://products.office.com/en-us/onedrive-for-business/switch-to-onedrive