is welfare fraud under three thousand dollars worth expediting to another state?

I am going to assume that you are asking if someone commits a larceny in 1 state and then moves to another, will the law pursue. Probably. The DA will go forward if they have the evidence and either file a felony complaint or get an indictment. They will try and contact the defendant. If they can't contact the defendant, they will get a warrant for the defendant's arrest. If the defendant is arrested pursuant to the warrant, he will be held for up to 90 days while the jurisdiction that got the warrant files papers showing reasonable cause to believe the defendant did the crime. Then the defendant will be picked up. Whether the prosecutor will go forward is anyone's guess.