Any account which is included in the business agreed to be transferred and is between the transferor and any person at any office or branch of the transferor in the State (or, where the relevant transfer order under section 33(1) so provides, inside and outside the State) shall be transferred or deemed to be transferred to the transferee on the transfer date and become as and from that date an account between the transferee and that person with the same rights and subject to the same obligations and incidents (including rights of set-off) as would have been applicable thereto if such account between the transferor and the person had continued and any order, instruction, direction, mandate or authority given, whether before or after that date, by that person in relation to such account or any obligation entered into by the transferor in relation to any person and subsisting at that date shall apply and have effect after the transfer of the account to the transferee as aforesaid, and any moneys owing on such account by that person to the transferor at that date shall become due and payable by that person to the transferee instead of to the transferor, and any moneys owing on such account by the transferor to that person at that date shall become due and payable by the transferee to that person instead of by the transferor.