Hello!
I'd love to tackle this project for you! I actually have experience using the Facebook SDK on Windows Phone, so I could complete this project in a short amount of time. By your original description and your update, it seems you want a proof-of-concept app that has a "Like us on Facebook" button. The user will click this button, be prompted to enter their credentials (which I'll store in Isolated Storage in case you need to do any other Facebook related tasks), and finally "Like" your company's Facebook page.
Here's a sample of the my previous experience in this area I mentioned: [login to view URL] That app authenticated a Facebook user and responded to any Facebook notifications the user would receive. The app also posted on the user's behalf.
Thanks for your time, I look forward to hearing back from you!