Employment Law Questions? Ask an Employment Lawyer.
I'm Lucy, and I'd be happy to answer your questions today.
It is not a crime to sign someone else's name with their permission. However, the crime of forgery require that you write someone else's name without authorization, usually with the intent to gain something of value. That's not what's happening here. A bank may reject a check or letter that you write on your boss's behalf, because they have his signature on file, and they can see that he didn't sign it. Once your boss tells them that he gave you permission to sign for the letter for him, you shouldn't have any issues. Or if you have an email where your boss gave you that direction, that could help.
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