Yep, in order to beat that record a secretary would have to be retained under at least 2 different presidents, not a very likely thing; a president is unlikely to keep his predecessor's appointment intact, at least not for very long, especially if his predecessor was from an opposing political party. There have been some secretaries that briefly served under multiple presidents, but it hasn't happened very often or for very long. The last secretary who has was Nicholas Brady, who was appointed by Reagan towards the end of his second term and also served under George H. W. Bush. Another interesting fact: Georgia Neese Clark, appointed as treasurer by Truman in 1949, was the first female US treasurer. Since then, every US treasurer has been female.
Yes, but two people beat Morgentheau's record as a currency signer. F.E. Spinner, the first Treasurer to be on modern currency, held the office from 3/16/1861 to 6/30/1875, a term of 14 years. The record holder, however, is one of Morgenthau's co-signers: W.A. Julian. His term lasted from June 1, 1933 (4 days before the gold recall) until May 29, 1949. His term lasted through all but three months of FDR's tenure, as well as Truman's first term. He probably would have served longer, except he was killed in a car crash in 1949. His term holds the record, lasting two days short of 16 years. This will almost certainly never happen again.