Brain-Teaser 692: First-class post

From The Sunday Times, 20th October 1974 [link]

On Trafalgar Day each of the five Sea Lords will take over a post now occupied by one of the others. Each predicts what will happen; those whose predictions are right will get more senior posts, and those whose predictions are wrong will get more junior posts.

The most junior speaks first:

Fifth Sea Lord: “Two Sea Lords will make a direct exchange.”
Fourth Sea Lord: “The Third Sea Lord will become the Second Sea Lord.”
Third Seal Lord: “A man who makes a true prediction will take over my job.”

Of the First and Second Sea Lords each predicts the same future new post for himself.

Which post is that?

This puzzle was included in the book Brain Teasers (1982, edited by Victor Bryant and Ronald Postill). The puzzle text above is taken from the book.