It doesn't sound right that they would not let him sign the extradition papers. That usually speeds up the transfer to Virginia. If they do not produce governors warrants by 90 days, he must be released. Speak to his attorney or hire one if you can! Good Luck!!
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Something doesn't make sense unless the judge is afraid they will pick him up and Nassau won't be able to pursue its case. His lawyer is in the best position to explain what is going on.
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Even if what you are saying is correct, your BF should send a letter to the court where he is wanted in Va. and advise that he wishes to face his charges and who has custody of him. It may be redundant if there is a hold on him, but speedy trial time in Va. will start running and they will have to decide whether to take him or not. But he does have a right to face the charges there if they want him. They may not have decided what to do yet, so are waiting to see.
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I doubt that the judge is objecting to him being extradited unless he has a trail scheduled or something unusual. Ask the lawyer that is handling the case, he will be familiar with the facts.