HMS Hope or HMS Moon
HMS Hope and HMS Moon both shared a depot ship of HMS Blake.
Service records show the same date range for the rating being on HMS Hope/HMS Moon.
HMS Hope was not at the Battle of Jutland whereas HMS Moon was and was in the 11th Destroyer Flotilla.
Some research has been carried out in the past but this does need to be verified as to its accuracy.
HMS Hope was an Acorn-class destroyer.
HMS Moon was an M-class destroyer completed in June 1915 and becoming one of the founder members of the 11th Destroyer Flotilla in September 1915.
In the same month, HMS Hope is listed as still belonging to 2nd Destroyer Flotilla (which shared the depot ship HMS Blake with 11th DF) but now a tender to HMS Vivid (Devonport).
By October, she was no longer listed under 2nd DF.
It seems likely therefore that crew transfer from Hope to Moon took place during September 1915.