He then undertook a postgraduate degree in Pharmacology at the University of Edinburghfunded by the Agricultural Research Council, under Alfred Joseph Clark.
[1] In February 1944, during the World War II Alexander joined the Royal Army Veterinary Corps and served in the Middle East.
In 1947 he returned to the UK and the Dick Vet School to study the physiology of the equine digestive system.
In 1952 he was appointed Senior Lecturer in Veterinary Pharmacology at the Dick Vet, which by then was part of the University of Edinburgh.
Alexander was one of twenty "shadow portraits" created in the Summerhall building of the college, depicting former Principals.