When you socket an item, the really does not creat a new item. It still keeps the original item as well as the rune/gem/jewle/whatever that you insert as two seperate items, identical to what they were before. What it DO change is that it links the items to each other. It markes the inserted item as being "socketed" and it marks the main item as having socketed items in it. Technically it will place the socketed items right efter the item it is insreted into in the linked list of items the game keeps for the character. The main item will have a number set telling how many items it has socketed (and thus follows it). That is really all that goes into it.
The same is basically what happens when you move items between your character, its inventory, the stash or the cube. The items aren't moved arround or anything, just a number (page) is changed in the item indicating were it is located. All items, regardless of what "page" is still kept in one big linked list and never moved arround except for socketing.
The id or fingerprint (or whatever else one like to call it) of an item is simply a random number (the current seed used to roll random numbers when the item was created) stored with the item. It won't change by the item being moved arround, marked as socketed and so on. It will be different after cubing an item though since cubing an item will basically destroy the original and create a new item from scratch (although often with certain aspects such as type and quality specified).
The "fingerprint" that is stored with the item was actually the initial seed used to randomly create the properties of an item, mostly the magical ones but also some others. Items was in earlier versions not saved with full stats but only with minimal information such as item creation level, base item type and the seed. When you entered a game, it would recreate the item based on this.
In later versions of the game, this was abandoned for various reasons. One was that it was not possible to change various aspects of item creation without morphing existing items, nor could one correct existing items in any way. What one did was instead to save the actual stats of items instead. The "drawback" and one reason why one initially saved items as their random seeds, all the way back to Diablo 1, was that saving stats, meant that anyone could (at least of realms) create items with stats at will since there was no need to get a matching seed correct. On the other hand, it had always been trivial to simply search for a seed that game the desired item anyway so not much protection.
Some basic items with no varying properties, such as runes, potions and so on, had no need for any seed at all since there was nothing to recreate so they never had this seed/finerprint assigned to them and not saved with them. However, it would be trivial to add it (and save it) for any item in the game should one desire. It do take up 4 extra bytes of saving space per such item, but it is perfectly possible later versions has added it. It would be possible to do it on the realms only, although it really serve no purpose to not have it as a general update but instead keep two different code bases for creation and saving/loading of items based on realm or other. The only reason would be if one allready needed such differences for other reasons and just did not want to apply the change to all items, but then, one could in a similar way remove the seed for bascially all items off the realm if one felt they serve no purpose other than on realms.
So to conclude, no, any fingerprint won't change by socketing any item, nor is any item really changed or replaced by some "socketed version". Hope this helped some.
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