Method for the preparation of a crystallized solid material of formula LiX x.2Al 3,nH 2 O, wherein n is between 0.01 and 10, and x is equal to 1 when X is an anion chosen from chloride, hydroxide and nitrate anions, and x is 0.5 when X is an anion selected from sulfate and carbonate anions, wherein the method comprises at least the following steps: a) a step of precipitating boehmite, in an aqueous medium, of at least one basic precursor chosen from among sodium aluminate, potassium aluminate, aqueous ammonia, sodium hydroxide and potassium hydroxide; and at least one acidic precursor selected from among aluminum sulphate, aluminum chloride, aluminum nitrate, sulfuric acid, hydrochloric acid, and nitric acid, wherein at least one of one of the basic or acidic precursors comprises aluminum, to obtain a boehmite suspension, the step a) operating at a temperature of between 5 and 35°C, and the amount of the basic precursor is chosen in order to obtain a pH of end of precipitation in the reaction medium of between 7.5 and 9.5, b) a step of filtering and washing the boehmite precipitate obtained in step a), c) a step of contacting the precipitate obtained in step b) with at least one lithium source, d) a filtration step of the suspension obtained in step c) to obtain a paste, e) a step of drying the paste obtained at the end of step d) at a temperature of between 20 and 80°C for a duration of preferably between 1h and 20h, f) a step of shaping the basic extrusion-mixed dough in which the dried dough resulting from step e) is mixed in the presence of a basic amount of between 0.5 and 3% by weight relative to the dry matter, wherein the dry matter is the weight of the dough resulting from stage e), dried in an oven at 200°C for 6 h, wherein the base is chosen from among inorganic bases and organic bases in solution, and in which the dough is then subjected to an extrusion step, g) a hydrothermal treatment step of the dried shaped material obtained at the end of step f), at a temperature of between 50 and 200°C and for a duration preferably of between 30 minutes and 12 hours. a) a step of precipitating boehmite, in an aqueous medium, of at least one basic precursor chosen from among sodium aluminate, potassium aluminate, aqueous ammonia, sodium hydroxide and potassium hydroxide; and at least one acidic precursor selected from among aluminum sulphate, aluminum chloride, aluminum nitrate, sulfuric acid, hydrochloric acid, and nitric acid, wherein at least one of one of the basic or acidic precursors comprises aluminum, to obtain a boehmite suspension, the step a) operating at a temperature of between 5 and 35°C, and the amount of the basic precursor is chosen in order to obtain a pH of end of precipitation in the reaction medium of between 7.5 and 9.5, b) a step of filtering and washing the boehmite precipitate obtained in step a), c) a step of contacting the precipitate obtained in step b) with at least one lithium source, d) a filtration step of the suspension obtained in step c) to obtain a paste, e) a step of drying the paste obtained at the end of step d) at a temperature of between 20 and 80°C for a duration of preferably between 1h and 20h, f) a step of shaping the basic extrusion-mixed dough in which the dried dough resulting from step e) is mixed in the presence of a basic amount of between 0.5 and 3% by weight relative to the dry matter, wherein the dry matter is the weight of the dough resulting from stage e), dried in an oven at 200°C for 6 h, wherein the base is chosen from among inorganic bases and organic bases in solution, and in which the dough is then subjected to an extrusion step, g) a hydrothermal treatment step of the dried shaped material obtained at the end of step f), at a temperature of between 50 and 200°C and for a duration preferably of between 30 minutes and 12 hours.