You would want to add the SFTP information for your child unit into your Parent BU as a 'File Location'. This can be found in the admin section under Data Management. This would require you to choose the location type of 'external SFTP site'. From there you type in the full FTP path of your child BU's SFTP as well as the corresponding Username and password.
You would then perform the data extract as you normally would. The file transfer you use to place it on the SFTP would then use the new 'Destination' you created via 'File Location'. This will place it into the specific folder on the Child BUs SFTP.
You can also have it stored inside of a Shared DE via the Parent BU if you just need a Data Extension to reference for the Child BU and don't need the actual file saved to the SFTP.