(a) A depository account may be transferred on the books of the depository only on presentation to the depository of:
(1) evidence of transfer satisfactory to the depository; and
(2) an application for the transfer submitted by the person to whom the depository account is to be transferred.
(b) A person to whom a depository account is to be transferred must accept the transferred account subject to the terms of the deposit contract, this chapter, and rules adopted under this chapter.