In 1940 the United States traded fifty mothballed WW1 Destroyers to England in exchange for land rights in areas of the British Empire. Were any of those fifty ships credited with sinking an Axis military vessel?
Yes, U boats. For a fuller explanation read "Hitler's U Boat War - The Hunters 1939 -1949" by Clay Blair. Below is an excerpt.
"One of the convoy escorts, the ex-American four-stack destroyer Montgomery, merely a month out of her overhaul and upgrade, spotted Marcel and attacked with guns and depth charges. The attack was successful; Marcel sank with all hands. She was the first Axis submarine to fall victim to one of the American warships transferred to the Royal Navy in the destroyer deal."
The raid was to destroy the Normandie dry dock in Western France, the only one large enough to repair German capital ships. Losing this dry dock meant the Germans could not send large capital ships out into the Atlantic as commerce raiders as they did the Bismark.
HMS Campbeltown was selected for her expendability. She was altered to look like a German destroyer, heavily armored, and had 4.5 tons of explosives set in concrete in her bow. Her mission was to bluff or fight her way past the defenses, ram the dry dock doors, abandon ship, and explode.
There is a well produced documentary on the raid which you may wish to watch before reading how it turned out. History spoilers!
The mission was successful, at an enormous cost, and Hitler's battleships never entered the Atlantic again, particularly the enormous Tirpitz. Instead, she was continuously harassed, damaged and eventually destroyed in Scandinavian waters.
It doesn't exactly follow the letter of your question, but it shows those destroyers weren't sitting around rotting somewhere and made a contribution to the war effort.
Generally served either as minelayers or convoy escorts. Their net effect was more as a deterrent. relatively little success against U-boats with a few notable exceptions.
These destroyers were collectively known within the Royal navy as the "Town class" and were provided by USA in five groups.
G.68 HMS Lewes - engaged E-boats Nov 42
G.27 HMS Leeds - engaged E-boats Feb 44
G.57 HMS Ludlow
I.42 HMS Campbeltown (rammed docks St Nazaire March 1942)
I.20 HMS Caldwell
I.23 HMS Castelton
I.35 HMS Chelsea (to Russia as Derzki 1944) - engaged unknown U-boat Feb 42
G.05 HMS Lancaster - Minelaying duties Icelandic waters
G.19 HMS Leamington (to Russia as Zhguchi 1943) - sank U-207 1941, U-587 1942
G.42 HMS Lincoln (to Russia as Druzni 1943)
G.76 HMS Mansfield
G.95 HMS Montgomery - engaged Admiral Scheer Nov 1940
G.88 HMS Richmond (to Russia as Zhivuchi 1944)
I.52 HMS Salisbury
I.95 HMS Wells
I.04 HMS Annapolis
I.17 HMS Bath -sunk by U-204
I.08 HMS Brighton (to Russia as Zharki 1944)
I.21 HMS Charlestown
I.49 HMS Georgetown (to Russia as Zhostki 1944)
I.24 HMS Hamilton
G.08 HMS Newark
G.47 MHS Newmarket
G.54 HMS Newport
I.57 HMS Niagra
I.07 HMS Roxburgh (to Russia as Doblestni 1944)
I.15 HMS St Albans (to Russia as Dostioni 1944) - Minelaying + sank U-401
I.65 HMS St Clair
I.12 HMS St Mary - Minelaying off Iceland
H.46 HMS Belmont
H.64 HMS Beverley - sunk by U-188
H.72 HMS Bradford
H.81 HMS Broadwater - sank U-boat Oct 1941, herself sunk next day
H.90 HMS Broadway - helped to capture U-110, sank U-89 1943
H.82 HMS Burnham
H.94 HMS Burwell
H.96 HMS Buxton
I.05 HMS Cameron
I.28 HMS Chesterfield - attacked U-268 1943
I.45 HMS Churchill (to Russia as Deiatelnyi 1944)
I.14 HMS Clare
G.60 HMS Ramsey
G.71 HMS Reading
G.79 HMS Ripley
G.58 HMS Rockingham - Lost by mine off Scotland 1944
I.81 HMS St Croix - sank U-87, sunk by U-90
I.93 HMS St Francis
I.80 HMS Sherwood
I.73 HMS Stanley - sank U-131 and U434, then sunk herself