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Pat PM the sender and let them know what you did and the date that you want to mail the book. If they come back with that is fine, then mark mailed just before it is ready to time out and mail the book as promised. Make sure that you send the PMs through transaction at this point it should be under the books to mail tab so the correspondence becomes part of the transaction history. If anything is said, pbs will be able to read that the requester agreed to the later mail by date - just make sure you mail it on that date.
The help docs say that if you can not mail it within 48 hours after the agreed mail by date you need to receive approval from the sender. That way you send it when you can and you do not break the rules.