Yes you can write him. There is a waiting period at these Diagnostic facilities as they put the inmates through a thorough testing period and there are some periods of segregation from the outside.
https://www.inmateaid.com/ask-the-inmate/can-i-write-my-brother-in-law-while-hes-in-diagnostics-in-jackson-and-when-will-he-be-allowed-to-write-and-call-me#answer
Accepted Answer Date Created: May 05,2015