Below, I suggest corrections to factual accuracy, grammar, spelling, and style. It's very possible that many of the errors are just typos or came about from being a little absent-minded. So, when I point out errors that are in fact errors of carelessness, I'm not trying to be mean or petty. And I'm not much aware of Hawking's biographical details, so I can say nothing about that.
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Stephen Hawking was born on January 8 1942
Insert comma after 1942
exactly 300 years of the death of Galileo. His parents were Frank and Isobel Hawking;
A period would be preferable to a semicolon
he had two younger sisters and
Remove the "and" and put in a comma.
Philippa and Mary, and an adoptive brother, Edward. They moved to St Albans,England
It isn't elegant to say where they moved to, unless you've previously mentioned where they lived before they moved. Perhaps, in your opening line, you could say where Hawking was born.
while when he was eight and he later went to St. Albans school when he was eleven. He went to Oxford University to study cosmology. When he was 21 he was diagnosed with Amyotrophic lateral sclerosis (ALS);
Capitalize the L and S in 'lateral sclerosis'.
when he was diagnosed he was
This is redundant. I would replace this segmet with 'and'.
expected to live for 2 years. Even though he expected to live for only 2 years
This part of the sentence is also redundant. You could instead use something like "Despite this knowledge..."
he married Judy Bachrach. They had three Children; they had one daughter, Lucy, and two son., Robert and Timothy.
Probably just a typo, but 'son.' should be 'sons'. The use of "they had" after the semicolon is redundant. 'Children' should not be capitalized. In fact, that entire first clause ,"They had three children," is logically redundant, given that they had a daughter and two sons.
He later wrote a popular cosmology book called a brief history of time.
The title of the book should be capitalized and italicized -
A Brief History of Time.
He wrote it because he needed money for his nursing cost and he wanted money to help pay for his children education.
That should be 'children's education'. Do you have a direct quote from Hawking where he gives these reasons for writing the book ?
His most famous work in cosmology is on black holes.
That's fine.
He discovered that the second law of thermodynamics, entropy could be applied to black holes which means that what has entropy has tempter has radiation and what has radiation means that it can emit light so he found that black holes aren’t black they glow.
This last sentence is incorrect in terms of the physics. But if you insist on keeping it, it is also grammatically wrong and could use splitting up into 2 or 3 sentences. And 'tempter', I think, should be spelled 'temperature'.
He became the lucasian professor of mathematics at Cambridge university a position once held by Sir Isaac Newton.
Capitalize L and P in 'lucasian professor', and U in 'university'.
He was been given many awards. He became a commander of the British Empire and became a companion of honor.
I would write is differently :
He has been given many awards and titles, including Commander of the British Empire and Companion of Honour.
Note the capitalization and spelling changes.
He works at Cambridge university.
In it's present form, this is virtually redundant. I would eliminate it, or merge it with the content of the other similar statement.
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