For what it's worth: 

Come to think about it, in that situation, I would consider preparing a "pre-emptive Notice CP01H response letter", by starting the correspondence (from client to the IRS) with a description of the error and the expectation of a Notice CP01H.  Include all the documents for the correction described in the IRS article (see my last post for the link.)  This may speed up the process.  If, after sending the pre-emptive response, client received the CP01H, send the same package with a cover letter and the proof of mail.  

Because the IRS is so much behind, no one knows what and when and how IRS matters would  progress..