If you previously purchased storage on your source account, you must also purchase additional storage space (prior to your migration) on the destination account or those documents owned by that user will not migrate properly.
Otherwise, your users will be missing some of the docs owned by the user who exceeded quota because that user has a larger source account than destination account. In order to complete the migration for that user and share the recipients with those docs the user will need to purchase additional storage on the destination account.
For additional information from Google please click on the links below:
Activate a Google Drive Storage License Subscription
Assign Licenses to Users