Why did Godfrey Ablewhite take the diamond to London in The Moonstone?
Godfrey took the Moonstone to London to pay off his debts.
Young Rachel is a woman of means, and her cousin Godfrey is interested. Cousins did marry in those days. I guess it kept the wealth in the family.
Rachel is also interested in Godfrey. Godfrey is good looking, and considered quite a catch. He is considered a philanthropist, but actually has quite a few debts of his own.
He was a barrister by profession; a ladies' man by temperament; and a good samaritan by choice. (ch 8)
Godfrey is not who he seems. He only wants to marry Rachel for money. Godfrey takes the gem to London, and is murdered there dressed as a sailor.
Seargent Cuff explains what happened.
[Lurker] has declared that the box did actually contain the diamond, called the Moonstone; and he has admitted having given the box (thus sealed up) to Mr. Godfrey Ablewhite…(Sixth Narrative, II)
The moonstone is never recovered, but Seargent Cuff successfully solves the mystery of what happened to it.