I must have had too much coffee... or not enough, but I am still not sure what you mean. If you have already installed the OEM then, technically, you are stuck with it since it is now tied to your computer. If you need to change/upgrade the motherboard at a later date you will likely have to call Microsoft to reactivate it [normally a 5 minute automated phonecall].
If your girlfriend's computer has a 64-bit CPU, then you should install the 64-bit version of 7. You will need to do a clean install [meaning you have to backup her stuff!]. If you aren't particularly bothered then you can upgrade her Vista to 32-bit 7 without her losing any data and programs.