applying for a job that is not posted

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I have recently found out that a job I would love to have is available. Problem is, the reason it's open is because they fired the person who previously held the position and they have not actually posted the position as being available. Now, that said, this is a non-profit group and the person who they let go was the only contact person I knew at the company. I have found a way of contacting the president of the group and I have his name, I guess I'm just not sure about what to say. Can I just send him a letter saying, Hi, My name is Jen and I heard that you fired your previous employee, I want her job? Obviously I would be a little more professional than that sentance sounded, but you get the point. I guess what I'm asking is how do I break the ice to get him to read my letter and resume?