I was a bit confused by GoingQuiet's answer until I remembered that the "lower" isn't the gun on an HK. But it IS what causes the gun to function as semi-auto or full-auto.
Your options, then, on an HK brand firearm is to have a registered sear or a registered upper.
So if the sear itself is the registered part, then obviously you can move it from gun to gun. But what GoingQuiet is saying is that if you move the sear from a short-barreled gun (which is fine when the sear is in it, because it's a machinegun, and barrel length laws don't apply) to any other gun, then the gun with the short barrel but no sear, suddenly becomes an unregistered SBR.
But if you have a registered gun (not sear), then it's the upper that is registered, because the upper is the gun on an HK. So imagine that you have a registered MP5 firearm. The upper is registered, but the lower contains the parts that make it full auto. If you remove the lower from the MP5 and put it on an HK33, then you still have a registered MP5 without a lower to enable to fire, and now you also have an unregistered HK33 with the parts to make it full-auto, but not the legal registration.
Hopefully GoingQuiet can correct my understanding if I'm wrong, but I think that explains the answer to the legal aspect of your question. As for interchangeability between the MP5 and HK33, I honestly just don't know, but I bet the answer is out there on the internet somewhere.
Aaron