prison@phuketprison.th.org
That is the email address for the Prison in Phuket
As far as I'm aware the provincial Prison is still the one in Phuket Town, Thanon Thamrong, Amphur Muang 83000.
Are we talking about a Thai or a foreigner?
Age?
I know my nephew got up to no good and was sent off to serve his time in Surat Thani. Depending on the offence phuket is not the biggest prison in the area. I remember there was a temporary prison in bangjo, Thalang, but temporary for what I can't remember.
Certainly try the email address and see where it gets you.
If I find out more I'll let you know