> you would be able to claim that as a work expense against your income
only if it was necessary for the job, and the employer would've otherwise paid for it.
But if the employer originally paid for an LLM, but chose not to now, i am not sure that you personally paying for one is tax deductible (might have to argue it out with the tax office).
But it looks like in the US, you would need to be self employed or own a business where it is an expense. Which is a bummer.