Arthur Cook was born in Gloucester on 11 July 1860 and joined the Portsmouth Division RMLI on 11 June 1879. Nelson was the flagship of the Australian station at the time. Her Wikipedia entry shows her moored in Sydney harbour. I bet Cook fell in love with the place and decided to stay, he had the right surname!
Definitely worthy of further research. The item "EGYPT MEDAL PAIR TO PTE ARTHUR COOK ROYAL MARINES BORN GLOUCESTER HMS RANGER" is in sale since Sunday, November 14, 2021. This item is in the category "Collectables\Militaria\19th Century (1800-1899)\Medals/ Ribbons". The seller is "mainlymedals" and is located in Newton Abbot. This item can be shipped worldwide.