[florida] Guy Is Threatening Murder-suicide On My Mom

I am writing to ask what steps my mom can and should take given this situation. TLDR: My sister's ex-husband hates my mom, recently checked himself into a mental hospital, where he told staff he wanted to kill himself and my mother. He was released from the hospital yesterday and she found this out via a call from the social worker.

Longer version: My sister's ex ("J", 48M) has some mental disorder, I believe bipolar, but also seems to have a personality disorder (narcissism, self-loathing), and substance abuse including benzo abuse. They have 2 kids together who my mom regularly babysits. J blames my mom for the divorce with my sister and everything wrong in his life, even though it's all been his own poor choices, alcoholism, etc that have led him where he is. He has trouble holding a job and frequently goes on benders. My mom has been incredibly helpful to him, my sister, and their kids, but J hates her and there is extreme animosity on his part.

Last week, he voluntarily committed himself to a mental hospital. He was released yesterday, with my mom receiving a call from a social worker who told her he made the statement that he 'wanted to' kill himself and her (my mother). The social worker specified that he "didn't have a specific plan" which I assume is why he was released.

I've long been afraid he would do something like this. He displays extreme bitterness toward my family combined with his alcohol and benzo benders (which cause loss of inhibition), he has frequently done things he later has to apologize for while on benders. But even while sober, he's suicidal and directs vitriol toward my mom and other family.

My mom is planning to get a gun, a dog, and security cameras. Questions: Can she report the threat to police? Does it count as a threat if he didn't say it to her directly, but comes from a social worker? Anything she can do to protect herself? I'm feeling very concerned, but I live in another state. Thank you very much for any advice on this unfortunate situation.