Conversation so far:
What was Luis Walter Alvarez's earliest work?
After he completed his oral exams in 1936.
Was it successful?
A telegram soon arrived from Gladys with a job offer from Lawrence.
Did he accept?
headed for California.
What did he do when he got there?
At the Radiation Laboratory he worked with Lawrence's experimental team.

Question: Did he marry?
Self-contained rewrite: Did Luis Walter Alvarez marry?