It depends on what the original copy of XP is. If its an OEM copy you will not be able to download any updates as its locked to the computer its on. If its a copy of XP created for the original computer ie a restore disk the same problem will exist. The only way this is possible is if both copies are full versions and even then you may have problem updating them which might mean contacting Microsoft to explain what you have done in order to revalidate both copies so you can download the updates. Before you even consider it therefore you will have to check to find out if both copies are full versions. If they aren't then you can't do it. I have an OEM copy of XP and its locked to the PC I am on. If I build a new computer I cannot transfer it across, it must die with the machine.
You can do it online or theres a phone number whcih unfortunatly I don't have the info on but I'm sure someone else will. I haven't actually tried this myself but it is my understanding that you need to contact Microsoft after you've altered it, certainly the online validation with Microsoft only takes a minute but what happens afterwards I don't know as I've never had to do it. Not being cheeky here but are you certain that both copies of XP are full versions? Do you understand what is meant by a full version? The only reason I am concerned is that if you buy a computer with windows preinstalled then normally to cut costs it is locked to that machine, either OEM or in the case of a laptop a restore disk specific to that machine with all the relevant drivers added on. Its a full version in that it has all the facilities of XP but it is not a full version in that you can only use it on that machine and are not allowed to transfer it to another computer. Not seeking to complicate things for you EARLR but thinking specifically about that laptop for example they normally come with a copy of XP locked to the laptop and you would not be able to use it on another machine.
Hopefully someone else a bit more knowledgeable about the ins and out of this can give better advice and a contact phone number for microsoft.