I asked my friend to inquire with his brother if there are any job vacancies.

Is this sentence- "Yesterday, I asked my friend to inquire with his brother if there are any job vacancies at his company." grammatically correct?

No.

"Yesterday, I asked my friend to ask his brother if there are any job vacancies at his company."

Kumarc said:

Is this sentence- "Yesterday, I asked my friend to inquire with his brother if there are any job vacancies at his company no full stop here" grammatically correct?

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Note my changes above.

@Kumarc The word "inquire" is one that native speakers rarely if ever use. If I were you I'd forget about learning it. I certainly wouldn't bother to learn how to use it. (It's not in my active vocabulary.)

Tarheel said:

@Kumarc The word "inquire" is one that native speakers rarely if ever use.

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I don't agree. Enquire/inquire is not rare in my opinion.