Equivalence of Shortest Hamiltonian Paths with a Starting Node to Traveling Salesman Problem

Q- Can someone explain the equivalence in detail please?

The correspondence is almost the same as your other question. Here, the starting node is specified, so you don't need a dummy node or dummy arcs out of the starting node. To go from H-path (with start $$1$$ and end $$t$$) to tour, insert arc $$(t,1)$$. To go from tour to H-path, remove the arc that enters $$1$$.