Hello and thank you for your question.
Although you did recommend this person, you do not have standing to act for your friend, so cannot pursue a claim against this woman on your friend's behalf.
Your friend could try to pursue a claim herself but if the amount in question is only $600 then it may not be worth pursuing, at least not to the point of litigation, as to pursue this through the courts would likely cost considerably more than the amount in question, and although if your friend were successful, she may recover some of her costs, it would likely be considerably less than the full costs.
That said, if she has provided you with an email which essentially admits to the damage, then it may be that a strongly worded letter, referring to her apparent admission and threatening legal action may be sufficient to pressure this woman into paying for or at least contributing to the cost of repairs, otherwise it may be commercially wiser to simply let the matter go.
I trust the above assists your understanding.
Good luck and please rate my answer.