If you select a file in your OneDrive for Business and then select the Copy option you’ll find some new abilities.
You’ll now see that you get the ability to copy to a SharePoint Online Team Site. You can read more details about this ability at:
Note - Scripting must be turned off for personal sites If scripting is turned on for personal sites in your organization, the Copy command is restricted to copying within your OneDrive.
At this point in time the functionality is only available with Copy and not the Move command. Also, at this point in time the ability is not available in Team Sites.
Thus, for the time being, you can now Copy (but not Move) via a browser, files and folders from OneDrive for Business to a Team Site (but not the reverse). Hopefully, the other abilities such as Move and inside Team Sites also is not far away.