Obtain email addresses who are in communications with inmate

I have the inmate’s written permission in hand, along with the inmate’s full name, ID number, the prison’s name, and the exact date range for the emails I need. What I lack is not being in the facility motherboard to get that info.

Im just wanting the emails whom the inmate account is communicating with. Not any info inside those emails.
Again i have permission in writing and notorized with inmate permission.