Hello, teacher, my friend has asked me to help her to write this letter of request. Can you check for grammar errors. Thank you.
I would like to take one month off work in January 2013 to visit my mother who now lives in Shanghai. I plan to use my two weeks leave for 2013 and am willing to take unpaid leave for two weeks. I have not seen my mother (85 years old) for almost three years. Please approve my request. Thank you.
Otherwise, your suggested message is absolutely fine with the exception of a missing apostrophe after "weeks" the first time it's used.
Remember - correct capitalisation, punctuation and spacing make posts much easier to read.