Thurgood Marshall, the first African-American on the Supreme Court, is credited with having had an important role in beginning the de facto desegregation of America's schools by successfully litigating the landmark case Brown vs. Board of Education.

A. with having had

B. for its having

C. to have had

D. for having

E. in that it had

This question is based on Idiomatic Usage. 

The word placed immediately before the underlined portion is ‘credited’

The word ‘credit’ can be used as a noun and a verb.

One gives credit to someone for something. In this sentence, ‘credit’ is used as a noun, as it is the object of the verb ‘gives’. 

E.g.: Sam gave all the credit for the arrangements to Melissa. (in this sentence, ‘credit’ means praise for or acknowledgement of an action)

The word can also be used as a noun to convey the meaning of being a source of pride.

E.g.: She is a credit to her parents.

The word ‘credit’ is also used as a verb. There are two verb phrases – credited to and credited with.

‘Credited to’ conveys the meaning of attributing something to some person.

E.g.: They credit the invention to him. The verb is generally used as such in the active voice.

‘Credited with’ conveys the meaning of considering usually favorably as the source, agent, or performer of an action or the possessor of a trait.

In this sentence, the verb ‘credit’ is used in this sense.

Option A is the only one that contains the appropriate idiomatic expression.

‘Credit’ in the verb form is not followed by the preposition ‘for. So, Option B can be eliminated.

If the subject of the sentence is mentioned as giving credit for having an important role to Thurgood Marshall, the preposition ‘to’ would have been suitable in the sentence. The sentence would thus be in the active voice.

E.g.: History credits an important role… Thurgood Marshall. 

Since the subject of the sentence is Thurgood Marshall and the sentence is in the passive voice, the phrase ‘credit with’ is more appropriate. So, Option C can be eliminated.

Option D also contains the preposition ‘for’, and so, can be eliminated.

Option E is idiomatically inappropriate and is wordy. So, Option E can also be eliminated.

Therefore, A is the most appropriate option.