There may be extra steps in between, but if you're tracking a transaction / relationship type which happens twice or more, you can expect that the person on the record is the person you're after or can point you at them.
But I don't know why they expect FBI to actually have it implemented. The system would have to be so widespread/common that we'd know if it existed. I mean, there's https://en.wikipedia.org/wiki/Currency_bill_tracking but that's for hobbyists. Otherwise banks may check for duplicate numbers... but I can't find any mention of more widespread tracking.
If say
* person A gets 100 banknotes from the bank, gives 50 to person B,
* person B pays 25 to person C and 5 back to bank (say, taxes)
* person C pays 5 of them to the bank
You can infer with some probability who traded what to who.
Certainly, though, those same businesses keep a lot of cash in order to give change to other customers. But that cash will still likely end up back at a bank before too long.
> banknotes are only in circulation for one or two exchanges before coming back to a bank
No, you don't get the 100% whole picture, but you can mine a ton out of data points like "note 38573204 was given to John Doe via ATM on 2023-01-10, and returned to bank by Jane Smith (owner of ABC Widgets) on 2023-01-14".