Can you "refer" an offer to another applicant?
Graduate programs don’t operate based on charity or friendship - admittance is based on merit. If you turn down the offer from B, the only rational thing for the administrators of that program to do after you turn them down is move on to the next person on their ranked list of candidates, if they still have room to admit more students, or simply write off your decision as one of the expected number of declinations they were assuming they would receive for this admissions cycle, if they have done the quite normal thing of sending out admission offers for more students than they actually have the capacity to accept.

In other words, all kinds of weird things can happen in some places that are poorly run or where for accidental historical reasons things run differently than in most places. It’s hard to prove a negative. But as a general rule, your friend is wrong and no such referral option exists.