答：本题两个he指代不明.句意不明,选项不全,网上找不到.答案不唯一.
请提供完整的题和出处.
此题句很有可能改自下文：
新概念三册对照译文Lesson22 By heart
.the gaoler decided to play a joke on his colleague to find out if, after so
many performances, he had managed to learn the contents of the letter by heart.
说明我的判断没有错,原题中的两个he不是同一人,作为单选题,应避免这个歧义.
从原文看,参考答案很可能是had known
不过正达美及热心网友从know的延续性心理状态的角度分析也有道理：
I know him. I got to know him ten years ago. I have known him for ten years.
I have got to know him.
get to know 是一个短暂的认识过程,know是稳定心理状态.尽管都译作认识, get to know与know是不一样的.前者是短暂动词,不可用于完成时的延续性用法,反过来,know是延续性用法,一般不用于完成时的结束性用法.不说：I have known him. 后需要加for 或since短语才完整.
其实有learn sth. by heart. 没有见过know sth. by heart的.
这是改题者的失误.
如果改用learn则用过去完成时最佳.为避免用两个he,前一个he用The gaoler较好：
The gaoler decided to find out if he had learned the contents of the letter by heart.
如果需要简写题句的话.
我想当然地说没有见过know sth. by heart,的,因为我将know 当作心理状态动词了.其实在这一词里就有：
One would expect them to know their parts by heart and never have cause to falter.
learn/ know by heart: 把……牢记在心
Eg.: The sentence is so important that you must learn it by heart.
所以：这里的know ... by heart =learn sth. by heart , 从by heat这个状语知道,know是行为动词
所以原题句
He(=The gaoler) decided to find out if he (= the aristocrat )had known(=learned) the contents of the letter by heart.
译：他决定弄清楚他是不是已经将信的内容牢记在心.