I’ve looked into this further but still do not have an answer. With the possible exception of friedo and me, no one appears to be very interested in this subject.
I looked at the balance sheets for several of the twelve federal reserve banks and, not unexpectedly, each bank lists the amount of Federal Reserve Notes outstanding for that bank. Also, and again not unexpectedly, the amounts outstanding for each bank varied significantly.
To avoid confusion, I think we should discuss exactly what it means when we say a Federal Reserve Note is issued. It is not when the note is tendered from the bank to one of its customers. (The customers of a federal reserve bank are the member commercial banks in its district). This is mere distribution. It is not when it is printed. A newly printed note is merely a piece of paper with ink on it that does not obligate anyone to do anything until it is issued. The aforementioned piece of paper with ink on it only becomes a Federal Reserve Note when a Federal Reserve Agent or an Assistant Federal Reserve Agent declares it to be an outstanding liability on the books of a particular federal reserve bank. This is when it is issued. (Before the nut cases start screaming, it takes more than just this declaration. The federal reserve bank must obligate some of its assets to the U.S. Treasury for the privilege of issuing a note.)
I also found this (https://www.federalreserve.gov/aboutthefed/chapter-5-federal-reserve-notes.htm) which did shed some light on the question. Prior to 1977, unissued notes were held at each federal reserve bank and were issued by a local Assistant Federal Reserve Agent. I would guess that prior to 1977, most or all of the unissued notes bore the name of the particular federal reserve bank that held them. After 1977, Federal Reserve Notes are issued by a Federal Reserve Agent or an Assistant Federal Reserve Agent when they are shipped from the printing facility in Washington, D.C. or Fort Worth, Texas.
Since issuing a note is actually an intangible accounting process on the books of the federal reserve banks, why would it matter which bank’s name is printed on a particular note? All issued Federal Reserve Notes are equally accepted by every federal reserve bank and the U.S. treasury regardless of which bank’s name is on the note. As an economist might say, they are fungible. I believe that the only reason the identity of the individual federal reserve banks are still on the notes is because of a legacy statute from the original 1913 Federal Reserve Act as amended. (See 12 U.S.C. § 413).
One might ask how are each federal reserve banks obligations accounted for when notes are withdrawn and destroyed because they are no longer fit for circulation. They are not counted or sorted by the names/numbers of the federal reserve bank written on each note. They are sorted by denomination. After destruction, a particular federal reserve banks reduction in liabilities is calculated using a ratio of the amount of that denomination outstanding for that particular federal reserve bank and the total amount of that denomination outstanding for all federal reserve banks. A small adjustment is made for obsolete notes such as Silver Certificates, U.S. Notes, etc. (Interestingly, denominations greater than $100 are handled differently and are sorted by federal reserve banks. This probably doesn’t happen much.)
All of this brings up another question. What do you think the ordinary person thinks when they hear that the government will just “print more money.”? I believe a lot of people take this literally. It is just a metaphor and a poor one at best. Almost all money is in a form other than currency or coin and creating more money has little or nothing to do with printing currency.