This applies to my wife. I am looking for advice on how she should approach a competitor for a not yet advertised position. The competitor will have this position because they just beat out her employer for the contract, she's losing her job as a result, and the competitor has no staff qualified to do this job.  

My wife works for a company that contracts with a state agency to serve students with disabilities. She travels around to different schools. Her job is only part time,. She visits students 1-2 times a week. The main office is 2 hours away, so she is essentially based out of our home. Which works well given her medical problems that I have written about and the fact that she is now 5-6 months pregnant. 

Her company's contract was put out for bid. After months and months of delays, she was told yesterday  that her company lost the contract for her territory, and her last day will be Friday. Through her network, she found out which company won the contract. This company has always refused to work with population of students in the past, and therefore, likely doesn't have any staff qualified to provide services. My wife already has relationships with those schools and students, and also relationships with the vendors whose technology she brings in.

So she's planning to contact them. She already found a staff directory on their website. But how should she approach it? Should she say her position is being eliminated? Should she congratulate them on winning the contract? She says she wants to write a cover letter just the way I do, presenting her credentials. I'll have to help her modify her resume this evening to point out all the technologies and things she knows, that this other company likely does not have.