There is no set timeline, and the experience varies more than most families expect going in.
The transfer out of county jail depends on two things that neither you nor your husband controls. The first is bed space at the receiving processing center. Federal and state processing facilities run at or near capacity constantly, and transfers happen when space opens up rather than on a fixed schedule. The second is the transfer schedule of whoever is handling transport, whether that is US Marshals, a contracted transport company like CoreCivic, or state-level transport officers. They move people when it is efficient for them to do so, not when it is convenient for families waiting on the outside.
From personal experience, my own journey looked like this. Eight days in county jail, then 89 days at a CoreCivic contract facility, then a one-night stop in Oklahoma City, and finally arrival at the designated prison. That entire sequence took the better part of four months from county to final destination. Everyone's path is different but the common thread is that it takes longer than it seems like it should and no one along the way seems to be in any particular hurry.
During the transit period, communication can be inconsistent. Phone accounts and commissary do not always transfer cleanly between facilities, and there may be gaps in contact that have nothing to do with anything he did wrong. Mail is often the most reliable way to stay connected during this stretch because it follows him through the system even when phones are not yet available at each new location.
Send letters, be patient, and check the BOP inmate locator or your state DOC offender search periodically to track his movement through the system.