Whether he mentions it or not, he will ask you what's wrong. Because the personnel department doesn't work for nothing, when he doesn't know how deep you are with B, he won't directly interrupt or refuse you in order to protect his position.
Then you say: What's my major? I am looking for a job now. B always said I should ask you. I wonder if your company needs it now?
Speak clearly and don't be careless. People just want to answer the phone.
Don't worry about him asking B. B is his boss, so it's not convenient for him to ask your directly. If you recruit for this position, he will ask you to show him your resume. If you don't talk, you may be asked to send him a resume. I'll let you know if there is any news. But you can't lie to him, just say that B is your friend. Even if you enter the company like this, one day he will know about your relations. No one will have a good impression on you then. Besides, if B is all your friends, he won't come to you personally, and HR is not a fool.