Shared mailbox is full

[mmchx]

Dear Expert,

I encountered on the shared mailbox is full. the thing is User tries to delete the mail on the deleted item and also on the recovery deleted item but the mail in the shared mailbox still full. Is the cause of this issue is about the permission of shared mailbox? 

I already assign the folder permission on the deleted item folder, but user still cannot delete the mail.

[#2]

Best grant him Full access, or perform the clean up with an account that has Full access permissions. Alternatively, increase the shared mailbox quota.