You're making us guess about a lot, but it seems reasonable to infer that your husband committed some new crimes while on probation and, as his probation is out of Georgia but he's been allowed to live in Louisiana, he's being held in a Louisiana jail pending possible transfer back to Georgia for probation violation proceedings. He may also be being held for his new criminal charges, and it may be that his probation violation issues won't be addressed until after his criminal charges in Georgia are resolved. It is very possible for a probation hold to be placed on an inmate being held on unrelated charges, in order to be certain that if he posts bond on his new charge he won't be released until probation violation proceedings are complete or he's allowed to post bond (if possible) on the probation violation charges. So it's possible that his present incarceration has nothing to do with his probation violation and everything to do with his new crimes. You have not given us anywhere near enough information to figure out what is happening.
Odds are your husband waived extradition when he was given permission to live in Louisiana. If so, then he would not be able to fight extradition to Georgia and it would be a matter of arranging transport from Louisiana to Georgia, perhaps to occur once his Georgia criminal charges are resolved. It also could be that the Georgia probation officer is waiting to see what sentence your husband receives on his new crimes as, depending on what they are and their seriousness, once the charges are resolved it may make more sense for Georgia to discharge your husband from probation as a violator than to transport him back to Georgia for additional proceedings relating to his underlying criminal offense.
Needless to say, your husband should be working with his lawyer.

