If you're thinking of literally removing a faulty SoC off your I9300 board and replacing it with the I9305 equivalent:
No. Don't do it. That's the worst idea I've heard in years.
If you're thinking of using an I9305 motherboard as a replacement for your I9300 board:
I started writing a very long post here about why you can't use most of the I9300 internals, but honestly it's neither interesting nor worth the bother to type.
In short, here is a list of things you can use from the I9300:
-The rear outer plastic case,
-Screws, gaskets, etc.
-Assorted minor components which didn't spring to mind.
You can't use the frame, or the antenna. You might be able to re-use the display, screen, and touchscreen controller; but have fun trying to remove the former two from the frame without damaging them or rendering them unusable. Heat guns are out, for a start.
Compared to buying a new I9305, you won't save much money, if any, and it might conceivably cost more to get all these things separately. It would also take you a lot of time, which carries its own cost.
Believe it or not, portable electronic devices bear little resemblance to cars.