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Won't be a problem since the CD-key will follow the case. However, you can have Oblivion installed and then play it without the disc so if he has another one he could boot up the old install with your serial using another disc but it seems unlikely he would do so (ie; you need a disc, doesn't matter whose disc, to boot up the game but you can take it out while playing).
If it comes to that though, Bethesda will sell you a serial if you ask them.