http://www.nmfs.noaa.gov/sfa/hms/rec_info.htm
Big Eye Threshers are protected
PROHIBITED SHARK SPECIES
The following sharks cannot be possessed or retained. If you catch a shark on this list, you must release it immediately into the water with minimal injury and in a manner that maximizes the survival of the shark. Recreational anglers may fish for white sharks using rod and reel but must release white sharks to the sea in a manner that minimizes injury to the shark.
Atlantic angel Squatina dumerili
Basking Cetorhinus maximus
Bigeye sand tiger Odontaspis noronhai
Bigeye sixgill Hexanchus vitulus
Bigeye thresher Alopias superciliosus
Bignose Carcharhinus altimus
Caribbean reef Carcharhinus perezi
Caribbean sharpnose Rhizoprionodon porosus
Dusky Carcharhinus obscurus
Galapagos Carcharhinus galapagensis
Longfin mako Isurus paucus
Narrowtooth Carcharhinus brachyurus
Night Carcharhinus signatus
Sand tiger Odontaspis taurus
Sevengill Heptranchias perlo
Sixgill Hexanchus griseus
Smalltail Carcharhinus porosus
Whale Rhincodon typus
White Carcharodon carcharias