(NO MP, not that I think this is MP-worthy, just that I believe in covering my ass)

So I mentioned in a comment earlier today that I am seriously pissed off with my job right now. I've spent 2 years working towards a promotion and keep getting platitudes, excuses, and half-truths instead. For the most part, I like my job, so I had resigned myself to slogging it out for another 6 months (until the next promotion cycle) before I made any decisions - besides, no one else in our group was getting promoted, so maybe those excuses had some truth to them.

Until last night. When I found out that not only did someone get promoted, that person is the most useless person in our whole group. And he's been there a shorter amount of time than three women I know who have been trying to get promoted (and he doesn't have prior work experience to make up for it either, he's straight out of grad school). He's basically our manager's mini-me, talking a smooth game while not actually doing any important work. Apparently the one piece I've been missing in my promotion efforts is a dick, and since I won't be getting one of those anytime soon, it's time to look for a new job. I know I'm going to run into this sexism & cronyism anywhere, but at least I can get paid better for doing it.


Which brings me to a question. There is a position that I want to apply for. It's a bit of a jump level-wise from my current position, but I would be completely suited for it. It would put me on a equal level with my current manager (and because of some collaborations between the new company & current company, I might end up working with him). Based on the job posting on LinkedIn, I know the recruiter for the position professionally. Our companies collaborated on an effort last month and I did work for her that she appreciated. Can I mention this is my cover letter? If so, how do I mention this in my cover letter? What do I even say in a cover letter (it's been awhile since I've had to write one)?