Perhaps a clue or hypothesis, rather than an expert answer to your question.
One HMS Cayman "was originally a Tacoma Class Patrol Frigate ... authorised as Gunboat (PG-186), she was redesignated Patrol Frigate (PF-78) on 15th April 1943." See Unit History: HMS Cayman
HMS Benbow is listed as "a Royal Navy shore establishment in Trinidad." Wikipedia, "HMS Benbow"
This challenge involves identifying "Caman." We don't know that there ever was a more complete descriptor (something other than just "Caman"). It is just speculation in this answer that Caman might refer to Cayman, as in the Cayman Islands. (I've so mistyped Cayman as "Caman" in this process at least once; so have others.)
During WWII, my father saw some duty at different temporary air fields. I first had to figure out where the field "had" been. Only then could I learn more about it. In that spirit, comments below follow the speculation that "Caman" is "Cayman."
- While it still does not solve the problem, a reference and passage (below item 2) outlines what seem significant changes in base administration and development occurring in the Cayman region just before Adrian's relative transferred. The changes mentioned are associated with a March 1941 "Lend-Lease" agreement between Britain and the US. (The attack on Peal Harbor doesn't happen until December, 1941.)
- "A DIFFERENT WAR: Marines in Europe and North Africa" Reports about marine units being "posted at several of the [Royal Navy] bases" that were "made available to the US," by the Royal Navy under the terms of the 1941 Lend-Lease. In this spirit, the the article refers to a "marine detachment" established at Grand Cayman. (Sadly, this statement was without further reference.)
See "Caribbean Islands-World War II"
At the outbreak of World War II, the United States assumed Britain's
defense responsibilities in the Caribbean. In September 1940, the two
countries agreed to the Lend-Lease Agreement ... [The US loaned forty
("out-of-date) destroyers in exchange for a rent free lease of]
British naval and air bases on five British West Indian islands--the
Bahamas, Jamaica, Antigua, St. Lucia, and Trinidad and Tobago--as well
as British Guiana, Bermuda, and Newfoundland. The Lend-Lease Agreement
was signed formally in London on March 27, 1941.
The introduction goes on to say that the under the lend-lease agreement, the US set up then eleven military bases in the area and it "quickly transformed five British colonies in the West Indies into outposts of Caribbean defense for use against German submarine warfare."
Other items for the file:
- According to a timeline about the area, "Milestones in our history," the first cruise ship (tourists) visited the Cayman Islands in 1937. And, between 1942 and 1945, "A U.S Naval Base and a U.S. coast Guard Base operate[d] in Grand Cayman." The same timeline reports that beween 1939 and 1945, a "Home Guard" was established for the Cayman Islands.
- "U.S. Naval Chronology of WWII, 1942" reports (a) May 01 (1942), "United States Naval Base and United States Naval Auxiliary Air Facility, Great Exuma, Bahama Islands, and United States Naval Base, Grand Cayman ... are established"; (b) July 13 (1942) "United States Naval Air Facility, Grand Cayman ... is established."
- Separately, brief reference to to the Caymans during WWII is found in the article, "Cayman Islands Seashore Vegetation..." [Geography" 25 (1982): 12], indicating "During World War II, the Cayman Islands were almost totally isolated for several years."
- A "Wreath of Remembrance" (about the Cayman Islands Veteran's Association) comments that, "For the men of Cayman, World War II Royal Navy Reserve duties focused around Trinidad in the southern Caribbean. That island was then the only source of oil for the British forces." It mentions supporting activities that were conducted on the island during WWII.
P.S. Neither of the words Cayman or Caman returned in my text query of Robert Jackson, The Royal Navy in World War II (Shewsbury, England: Airlife, 1997).