Det Centrale Personregister - Wikipedia, the free encyclopedia - it's basically a Danish identification number, similar to the Social Security Number of the USA.
It's assigned to everyone with the residence permit and the Danish address, and it's required almost everywhere (tax office, banks) so your friend surely has it. When i've mingled with CBB's webpage I've stuck on the form which required the CPR and the delivery address, so I don't know what's next, but I presume that those two things will suffice to get the SIM.
I think that the CPR is required only for limiting the number of SIMs in special offer per person , and if you'd buy it without this offer you wouldn't have to have it, but it's only me thinking - the page is only in Danish and Google's translation tool is not that great