The only thing I would have added was the the person listed as the remitter would have signed the check under the phrase "Not Used for Purpose Intended." Where the practice came from? What justifies it? Does it work only because there is no one to complain about it? I have never known. John might, so I'll see if I can rouse him.
In any case, it is a common practice among banks and, yes, I believe it to be correct.
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In this world you must be oh so smart or oh so pleasant. Well, for years I was smart. I recommend pleasant.