It takes a couple of days through the mail. Once it arrives in the mail room it is up to the staff to read the mail and determine when they hand it to the inmates at mail call
https://www.inmateaid.com/ask-the-inmate/i-just-sent-a-postcard-to-an-inmate-how-soon-will-he-get-it-and#answer
Accepted Answer Date Created: December 24,2015