There is no fixed timeline for the transfer, and that is one of the more frustrating realities families deal with after sentencing.
The time your person has already spent in county absolutely counts toward the three-year sentence the judge imposed. Every day in county custody is credited regardless of whether the facility is classified as a jail or a penitentiary. That credit does not disappear when the transfer happens.
As for when the actual transfer occurs, that depends entirely on bed availability at the receiving state facility and the transfer unit's schedule for that region. State prison systems operate on their own logistics and do not publish transfer dates or timelines to families. It could happen in a matter of weeks or it could stretch into several months. There is nothing you can do to accelerate it, and calling the facility repeatedly asking for a date will not produce one.
On the work release question, a split sentence does create a pathway to work release, but it is not automatic and it is not early in the sentence. Inmates who maintain completely clean disciplinary records and demonstrate model behavior throughout their time become candidates for work release consideration as they approach the end of the sentence. Facilities use work release as a reentry vehicle, a structured transition back into the community before full release. The key phrase is near the end. Getting there requires years of clean conduct first.
Encourage your person to start building that record from day one. Every incident report makes work release less likely. Every clean month makes it more likely.