How to transfer salary to another bank after I signed an MoU to buy a property on mortgage?

Hi,

I have recently signed an MoU to buy a property and a bank has offered me a good loan package so I want to sign with them.

Therefore, I have asked my employer to produce a Salary Transfer Letter (STL) to be able to sign my loan with this bank.

Just to clarify, I have no loan with any bank, I just have a credit card with my current bank (never had any issue on it). To produce the STL my employer needs a non-objection letter (NOL) from my bank or a No Liability Letter (NLL).

My current bank said the first option is impossible as "they do not have a template for that" and they can only produce a non-liability letter (NLL), however, this is not possible as it takes 45 days after card's cancellation to get the NLL.

My question is: Does my employer really need a NOL or NLL to be able to transfer my salary to another bank? (He never signed anything with my bank).

Employer says there is a tacit agreement between employer and bank when the salary gets transfered to the bank, is that true?