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I have been there this year in April - you do need a license ($10 Euro/month, ask in the administrative building - I received some contradictory info about where to get it on the island of Faial but found it).
Go to Azores | Whale Watching, Scuba Diving, Fishing Tours, Boat Tours | Faial and Pico and ask there. Norbero himself (the owner) spearfishes and knows the spots. In general it is best to go late summer and be taken by boat to pinnacles to get pelagics. Off the shore you can get mullet, dentex, maybe amberjack. Water temperature will be around 17 degrees and in late summer the water should be very clear. I did hear about the groupers, too. I believe you can not have more than 5 fishes on you at any time but verify locally