Identify A and B

Ether when treated with $\mathrm{HI}$ produces both benzyl iodide or phenol. Under acidic conditions (i.e., with a small amount of HI), the ether can undergo an acid-catalyzed cleavage to form phenol  and benzyl iodide. In this reaction, the $\mathrm{HI}$ acts as a catalyst, and the protonation of the ether oxygen atom makes it a good leaving group, which then departs to form benzyl carbocation. The carbocation can then react with the iodide ion to form benzyl iodide, while the protonated oxygen atom can undergo deprotonation and form phenol.