Let $\mathfrak{g}$ be a basic classical simple Lie super algebra. I want to prove that every finite dimensional module over $\mathfrak{g}$ has a highest weight vector.

My feeling is, since $e_i$'s are rising operators it will kill a non-zero vector and this will give us a highest weight vector and may be we need to use Lie's theorem.

But I am unable to connect these things to get a perfect answer. If some one can tell me clearly what is happening here, that would help me a lot. Thank you.