The public folder has to have an out of office message enabled. But it cannot receive any email, as requested by the client it is a 'no mail receiving' inbox. Can this be done?

Your Public Folder is on a permanent vacation? An OOF on a PF doesn't make much sense. Also, why mail enable it in the first place if it is not to receive any emails? You may want to consult your client once more as it doesn't sound like a proper way to go.

Anyway, you can set up an auto-reply and then delete the incoming message it has responded to.

I'm not entirely sure but the company uses the public folder system, and not group mailbox. Anyway, they requested it to be a 'no reply mailbox' but they need to have the automatic message saying that 'any message sent to them will not be received'; the thing is that they do not want to receive any emails in this box. Is there any option in the public folder for Exchange to block incoming mails for a public folder that is mail enabled?

Anyway, you can set up an auto-reply and then delete the incoming message it has responded to

Hi,

I suggest the same as Robert did.

Anyway, if your request is on Exchange, please post the question in Exchange Server forum:

https://social.technet.microsoft.com/Forums/office/en-US/home?category=exchangeserver

Regards,

Melon Chen
TechNet Community Su