Let's say that person A mined some bitcoins, so now all the payment fees for those bitcoins goes to him. Person B wants to buy from person A the right to receive those payment fees.
Is it possible to safely transfer "mined rights" from person A to person B?
I think you're mixing some things up. When you mine a block, you decide which (outstanding) transactions to put in it. As a reward, you get 50 BTC + all fees from the transactions you put into that block. There is no such thing as "mined rights", and you don't get fees from transactions using the 50 BTC you received as reward; those go to whatever miner puts those in a block.
You can simply do a payment of 50 BTC + the fees you got from mining, to someone else.
