In the book by Muhammad Abdul-Haqq Ansari (on page 85), it is mentioned: "Allah reveals about the Unseen to a man and asks him to convey that to others, he is a prophet and messenger. But He does not ask him to preach it to others, he is a prophet, not a messenger."

Kindly shed some light on the underlined text. Isn't it the duty of the prophets to preach too?

There exists a difference of opinion amongst the scholars. This is an opinion, but the correct opinion is that they are ordered with conveying but they don't have a new Shari'ah.