Presumably the "1963" Herald is commission number GA80001 or higher, or possibly GB1 or higher. Either will have the "Mk2" or "Star" chassis frame, with engine mounts on the suspension turrets. This being the case, the swap is direct.
Of course, your "1963" could have been a slow car to sell when new, and it might just be that "Mk1" chassis. If so, worst case scenario is that you'd have to swap front engine plates to get the proper mounting for that chassis.
I'm also going to guess that the "1965" engine is a GD series and that the "1963" engine is a GA series. The GD series engines had somewhere between 48-51 hp as opposed to the 40 hp of the GA series. That's not enough to overly strain the early chassis!
Also, both gearboxes likely are GA series, so they'll be the same.
PM me if you have specific questions about any/all of the numbers I'm referencing.