There is no set timeline, and that is the frustrating reality of transfers within the county and state system.
Once a sentence is handed down and a placement is determined, the facility needs two things to move him: an available bed at the receiving location and a transport arrangement. Both of those depend on factors outside anyone's direct control. If the detention center has open beds and a transport run scheduled soon, it could happen within days. If beds are tight or transport is backed up, he could sit in county for several more weeks.
A year in county jail waiting for sentencing is already a long stretch, and that time should be credited against his 180 days depending on the jurisdiction. That is worth confirming with his attorney if it has not been addressed already. In many cases the time served calculation means he is closer to the end of his sentence than the 180-day number suggests.
In the meantime, his status and location in the system should update through the county's inmate locator once the transfer is processed. Keep an eye on that, and if communication goes quiet for a period after he moves it is likely just the standard blackout that happens during transit and intake at the new facility. It typically resolves within a few days once he is settled and has phone access again.