They ask who made the tube, how it was made, and material used. They inspect the bore with an endoscope to see its condition. Any flaws in the bore such as cracks or cavities would cause it to be rejected. They also check to see if the tube has the correct dimensions. You indicated that the barrel you are getting is cast solid and vertically. This is the best process as any flaws in the casting are usually found in the center of the casting and they will be removed during the machining process.
If you use a projectile in this tube, make sure that it does not exceed the weight of a shell. This gun was not designed to fire full weight, 12 lb shot.