My boyfriend is currently locked up in l.A county for 3-4 months on driving on a suspended and then he'll be extradited back to Arizona to face some charges. Someone told him about this interstate agreement on detainer something about he'll have the right to a speedy trail. So I'm wondering what exactly is this form and how do I get one to send to him

Yes once he has served the first sentence, and is extradited back to Arizona he can ask for a speedy trial.