In the Declaration of Independence, when it uses the word "he," who is being referred to?

The "he" is George III, King of Great Britain at the time. Jefferson references him in the sentences that immediately precede the list of grievances.
Historians interpret George III's life and reign in wildly different ways. It is no longer in fashion to see him as either a mad incompetent or a terrible tyrant, but there are many older biographies that present him in that fashion. He is still probably best known to laypeople as Mad King George, due to the mysterious illness that affected him in his older years and eventually left him unable to serve as king. His illness served as the basis for a play by Alan Bennett, The Madness of George III, which in turn served as the basis for the well-regarded 1994 film The Madness of King George.
Contemporary historians take a more balanced view, and pay as much attention to the successes of George III's reign against France as they do to his role in losing the American colonies.
Why did Jefferson spend so much time referring to George III? It was part of his rhetorical strategy. The Declaration of Independence is rightly renowned for its rhetorical flourish, and the section summarizing the "abuses" of the king is one of the highlights of the text. Jefferson uses repetition (more formally, parallel structure and anaphora) to summarize the colonists' grievances. He also draws on the common and recognizable theme of tyranny to create sympathy for his cause. (In reality, some of the grievances Jefferson lays at the feet of George III could have been attributed to Parliament as well.)
https://www.archives.gov/founding-docs/declaration-transcript