Presenting a letter to a bank purporting to be from your employer that you typed up without the say-so or the approval of your employer would be ... ill-advised to say the least. Even if they didn't check up on it, you are consciously and intentionally deceiving the bank, no matter how honest the contents of the letter or how promptly you inform your employer of it, etc., it has not actually been authorised by them when you present it. I agree with PinkyBear, it is evidence of employment and income that they are looking at, if that can be provided by the business (rather than by the individual you report to) then it should satisfy the bank.