The normal time it takes is between 1-3 days. Once the letter is received by the prison intake, they open and examine the contents for contraband. Every prison has their own procedures which might effect the actual date the inmate receives the letter.
https://www.inmateaid.com/ask-the-inmate/how-long-does-it-take-for-an-inmate-to-recieve-a-letter-from-inmate-aid#answer
Accepted Answer Date Created: April 14,2013