@a82rivers yes the short block (the engine itself) is the same no matter which transmission it came with, However, you'll need to swap a few parts over.
The autos come with a pressure plate, compared to the manuals come with a flywheel.
Also, the EX civics had a slightly different intake manifold. The Manuals came with the idle air control valve on the back of the intake, compared to the automatics had the idle air control valve on the side of the throttle body.
If you still have the original engine, then it should be pretty easy. Just swap the pressure plate for the flywheel, and reuse the intake manifold that came with your car.
A little tip: Most Honda's came with a timing belt, and those belts should be replaced every 100k miles. If you don't know how old the timing belt on your donor engine is, I would recommend replacing it (and the water pump). It's not expensive, and it's 10x easier to do it while the engine is out of the car.
Let me know if you have any more questions!