If I were a tech, and faced with the challenge of determining if a Mk. III style mag. housing was a welded over original or a newly made duplicate, I would study how the housing had been made. Originals were formed using tools likely not available to a home builder. Toolmarks would be in evidence. There would also likely be traces of the resistance welds where the box had been attached to the original casing. If the casing tabs were left in place, and the tabs themselves welded to the new tube, it would be apparent. If an original box were welded over, there would be several areas of weld - the STEN MC MK III on top, the LB, serial and /l\. It might be possible to do this much welding in a manner that a well equipped crime lab. could not detect it, but I wouldn't bet the farm on it. If there was any suspicion that an effort was being made to deceive, the techs would have a really close look.
Best procedure to follow would be the one Stencollector illustrated with his photos - a photo record of the housing being scratch built.