Moving does not follow the same schedule as the law. In fact, few things do. The law is a very slooooow process. Nevertheless, you have to prioritize any criminal case over your need to relocate.
Moving with open charges against you is a bad idea. If you skip states, or sometimes even counties, depending on the charge and conditions of your release, then you are opening yourself up to a warrant being issued for your arrest, possible revocation of your release, and a stiffer sentence.
Additionally, though you might say, “well, whatever, I’m in a different state,” some states will cooperate in arresting and returning people with open criminal cases. Additionally, an outstanding warrant in one state can prevent you from getting a driver’s license and other privileges in another state.
Above all else, that case doesn’t just go away. It will remain on your background check for all employers to see.
In others words, even though it might be a drawn-out process that hampers your move, close your criminal case and pay the punishment before you move.