How to translate 'They made her make him give me the book'?


How to translate 'They made her make him give me the book'?

Can I translate it to:

Karera wa kanojo ga kare ni sono hon o watasi ni watasaseru you ni saseta.

彼らは彼女が彼にその本を私に渡させるようにさせた。




"They made her" is 彼らは彼女にさせた. What did they make her to do? It is "She make
him give me the book(彼女が彼が私にその本を渡すようにする or 彼女が彼に私にその本を渡させる。)

They combine and it becomes 彼らは、彼女に彼が私にその本を渡すようにさせた or 彼らは、彼女に彼にその本を私に渡させた.

