Failover in MySQL Chain Replication
You're not switching sources so there is nothing required to migrate from an A master to a B master.
To clear up the record of A being a master of B however the following may be desirable:

(B) STOP SLAVE will stop (B) from trying to get more binlog events
(B) RESET SLAVE ALL will make (B) forget about the (A) master.
(B) RESET MASTER is wrong. (B) is the master of (C). It was even before (A) is removed.