Hello, Lawrence-- and welcome to English Forums. I have corrected your letter below, but as an aside, I should comment that the trend toward using more contract staff and fewer permanent employees is worldwide and accelerating. Your letter is not likely to accomplish what you would like it to.
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"Thank you very much for taking the time to consider my request. I will work hard to merit your trust in me by giving me the opportunity to become a permanent employee.
Sincerely yours, "