The hardest part of this answer is that your ability to influence his physical placement from the outside is extremely limited, and calling the classification center to request a move is not something that carries weight in the way you might hope. Facility placement decisions belong entirely to the corrections department, and outside requests from family members do not typically move that needle.
What can actually help him is action on his end, and he needs to take it now.
If he genuinely fears for his life, he needs to go directly to the captain or lieutenant on his unit and ask to be placed in protective custody. That request needs to come from him, in person, stated clearly. He does not need to prove the threat at that moment. He needs to say the words: I fear for my safety and I am requesting protective custody. Staff are required to take that seriously and respond.
Protective custody is not comfortable. It typically means restricted movement, limited privileges, and separation from general population. But being alive and in PC is better than the alternative he is describing, and he needs to understand that requesting protection is not a weakness, it is the system working the way it is supposed to work.
From your end, you can call the facility and ask to speak with his case manager or a lieutenant and express that your son has communicated fears for his safety. Do this calmly and factually. You cannot compel a transfer, but putting a documented call on record that says a family member reported safety concerns creates a paper trail that matters if something goes wrong. Keep the tone concerned and cooperative rather than accusatory.
The most urgent message to get to him through any channel available is this: report it to staff today, ask for protective custody today, do not wait.