I'm not sure I'd want to order the birth certificate for the entry you've found just yet, as it doesn't look as if you have enough information for it to confirm anything for you. Yes, it might just be that the birth date matches, but apart from that and the first name being the same, would it convince you that this is the original birth certificate for your friend's mother? Even her first names could have been changed in the adoption process.

Personally, I'd recommend looking again at the adoption papers, as Megan suggested, and trying to follow up with the adoption agency. Apologies for casting doubt on what you've found so far, but I've been down a similar road before and it didn't turn out very well unfortunately because I made too many well meaning assumptions! :-)

Christine