Jefferson was out of the country when the Constitution was written.
Well, if you want to get picky (as I generally do), that “life, liberty, and the pursuit of happiness” thing was in the Declaration of Independence, not the Constitution, and Shakespeare’s “green-eyed monster” was jealousy, not envy. There are other factual errors as well in just the parts of the book quoted.
I don’t think I’ll waste my time reading it.
While Jefferson was minister to France at the time, the statement is nevertheless correct.
Jefferson had important allies at the Constitutional Convention, the most important of whom was James Madison, and with whom he was in frequent communication.
Jefferson's draft of the Virginia Constitution was also an important influence on the Federal Constitution as well. Jefferson's Virginia Charter of Religious Liberty was integral to creation of the First Amendment, Jefferson was insistent on an explicit recognition of something like the Second Amendment and an explicit Bill of Rights as well.