Make the sauce first. Heat the olive oil in a skillet over medium-high heat. Add the garlic and the shrimp and cook until the shrimp turn pink. Remove and discard the garlic. Remove the shrimp and set aside.
Add the sherry, lemon juice, and stock, and bring to a boil. Reduce the liquid to about one-third the original volume, then remove from the heat.
Cut the stick of butter into small chips and whisk them in to make a creamy-looking sauce. Stir in the parsley, then add the crabmeat and the reserved shrimp. Set aside in a warm place.
Mix the salt and pepper into the flour. Dust the trout fillets liberally in the seasoned flour.
Heat the 1/4 cup of olive oil over medium-high heat until it shimmers. Saute the trout, two fillets at a time, until golden brown--about three minutes per side.
Place a trout fillet on each serving plate and top with the sauce, splitting the shrimp equally among the plates.