If they are in a county jail, then yes they are moved to a Federal Bureau of Prisons (BOP) facility depending on the security level designation decided during the period before movement.
https://www.inmateaid.com/ask-the-inmate/are-federal-inmates-always-moved-to-a-different-prison-once-they-recieve-their-sentence#answer
Accepted Answer Date Created: October 29,2015