Here is the sample letter to last lady. Be sure to add your own

It would be the best to add as much as your own and specific information to explain what's your research area, contribution, your personal concerns etc.....
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The White House
1600 Pennsylvania Avenue NW
Washington, DC 20500

Subject: Expedite Name Check Request for Green Card

May XX, 2007

Dear Mrs. Laura Bush,

My name is XXX, a scientist working for XXX. I am writing this letter asking for your help to expedite name check procedure pending at FBI. My name checking has been consistently pending for a length of nearly 2 years and it is much more than normal. My family (I, my wife, and our 9-year-old son) have been waiting for the green card, which couldn’t be approved due to the unfinished name check.
I am doing research in XXX diagnosis. Our lab provides XXX results of assessing a woman's risk of developing XXX cancer based on XXX. This test has become the standard of care in identification of XXX. Our results have changed life of thousands and are going to continue benefit American women.
A green card would help my American dream become true and it will facilitate my contribution in the research and benefit more American Women eventually. However, I am deeply frustrated by the name check pending. Although I fully understand the name check is an important step in securing this country.

Your help on this matter would be highly appreciated.

Here is my information:
Name: XXX; SSN: XXXX; Date Of Birth: XXX
Alien Number: XXX; I-485 Receipt Number: XXX


Sincerely,
XXX