It takes 1-3 business days but once it is received in the mail room at the jail, it is up to the mail room staff to hand the mail out to the inmates. It's hard to pinpoint an exact time for that reason
https://www.inmateaid.com/ask-the-inmate/how-long-will-it-take-for-an-inmate-to-get-a-postcard#answer
Accepted Answer Date Created: April 20,2016