The following non-delivery report:

The recipient's mailbox is full and can't accept messages now. Please try resending this message later, or contact the recipient directly.

MailboxFull

means that there is a storage limit set on the recipient's mailbox and it is currently full.

The Diagnostic information for administrators section also contains the following error:

554-5.2.2 mailbox full 554 5.2.2 STOREDRV.Deliver.Exception:QuotaExceededException.MapiExceptionShutoffQuotaExceeded

QuotaExceededException

 If the recipient is hosted in the same organization as the sender, the issue can be resolved either by:

If the recipient is hosted outside of your organization, contact the recipient directly and provide their mail administrator with the bounce back message.