Is the bank liable to the payee for depositing and encashing the crossed checks to an unauthorized person?

Yes. The effects of crossing a check relate to the mode of its presentment for payment. Under Sec. 72 of the Negotiable Instruments Law, presentment for payment, to be sufficient, must be made by the holder or by some person authorized to receive on his behalf. Who the holder or authorized person depends on the instruction stated on the face of the check. The checks here had been crossed and issued “for payee’s account only.” This only signifies that the drawers had intended the same for deposit only by the person indicated (Associated Bank v. CA, G.R. No. 89802, May 7, 1992).