Hi Marcus!
What I'm getting from your question in that a high-authority site has a roughly two-week-old page featuring a piece of content of yours. Is that correct?
Generally, a PA or DA of 1 simply means that we don't yet have information on that URL. As I explained in my response to John, we gather that information through our crawl of the web as documented in our Mozscape index. That crawl takes ~1 month.
PA and DA are based on pretty much the same factors, and those factors are almost entirely based on the strength of the backlink profile. According to the Open Site Explorer home page, the last index was released March 2, and the next index is expected to be released March 30. That makes March 30 the earliest you can expect to see information about that page. It's quite possible that you still won't see it until the following update.
PA and DA are both based on pretty much the same factors, and those factors are based almost entirely on the strength of the backlink profile. The difference is that DA is based on the backlink profile for the entire domain, while PA is based on the backlink profile for just that page. PA can be raised by building links to the page. If it doesn't gain links, PA won't improve (though I'd expect it to me higher than 1 once it's been crawled and indexed).
Now, lastly, you ask about your boost in the SERPs. I assume you mean you're expecting a bump for your site, since the high-authority site links to you through the content it's picked up, yes? In that case, you may see some benefit on the SERPs well before the change is reflected in PA (Google crawls a lot faster than we do). The amount of a boost you get will depend on a lot, including your competitors' link profiles and whether the content that got picked up also appears on your site (if it does, I hope the high-authority site is pointing to the original content on your site with rel=canonical, or you could find yourself competing with them).
I really hope that makes sense. Let me know if you need more clarification, or if I'm just totally misunderstanding your question! 