in there = there
Your sincerely = Yours sincerely
But did you want also a "formal" letter?
Dear Professor .....,
Could you please train my student while she is in London? I would like her to have a practical training in there. It would be her opportunity to experience work with academics and research, because she has been expecting to do research in the future. She could be helpful for you in order to do the research of IT.
The student is expecting to start the internship from November 1, 2007 to February 28, 2008.
Thank you very much
Your sincerely,
.....(name)......
in there = there
Your sincerely = Yours sincerely
But did you want also a "formal" letter?
You might be interested in this page about Formal Letter Writing
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I'm not a teacher, so please consider any advice I give in that context.