NOVELTY - The process comprises adding a lithium transition metal oxide-containing fraction to stoichiometric amount of sulfuric acid with a concentration of 1-2 mol/l in a solid to liquid ratio of 25-65 g/l to reduce the transition-metal content in the solution containing stoichiometric amount of hydrogen peroxide and then to form lithium sulfate at a temperature of 35-65 degrees C, separating sulfates of the transition metals containing solutions and then washing remaining for three times, and adding the separated sulfate and sulfate-containing washing solutions to precipitate hydroxides to be separated.    USE - The process is useful for hydrometallurgical recovery of lithium, nickel and cobalt from the lithium transition metal-containing fraction, used in galvanic cells, to produce a product including lithium transition metal oxide or lithium transition metal phosphate that is useful as active cathode materials in lithium-ion batteries (all claimed), which are useful in mobile electronic devices, in an automotive industry and for hybrid drives or purely electric drive and back-up power applications.    ADVANTAGE - The process allows recovery of lithium from the fraction in an economical and energy efficient manner and production of the lithium salts with high purity thus providing high power rechargeable batteries with improved stability and energy density and less-self discharge rate.    DETAILED DESCRIPTION - The process comprises adding a lithium transition metal oxide-containing fraction to stoichiometric amount of sulfuric acid with a concentration of 1-2 mol/l in a solid to liquid ratio of 25-65 g/l to reduce the transition-metal content in the solution containing stoichiometric amount of hydrogen peroxide and to form lithium sulfate at a temperature of 35-65 degrees C, separating sulfates of the transition metals containing solutions and then washing remaining for three times, adding the separated sulfate and sulfate-containing washing solutions to precipitate hydroxides to be separated, washing the remaining lithium sulfate-containing solutions, and converting the solutions into lithium hydroxide by an electrodialysis process with bipolar membranes. The transition metals include nickel, cobalt and/or manganese, and less than 1 wt.% of aluminum, and have a particle size of 100-400 mu m and a pH of 9-11. The method further comprises adding the lithium-transition metal oxide-containing fraction to stoichiometric amount of hydrochloric acid having a concentration of 1-2 mol/l to reduce the transition-metal content in the solution containing stoichiometric amount of hydrogen peroxide and to form lithium chloride at a temperature of 35-65 degrees C, separating chlorides of the transition metals, washing the remaining residue for three times, the adding separated metal chloride and metal chloride-containing washing solutions, precipitating hydroxides, washing the remaining lithium chloride-containing solutions, and converting the solution to lithium hydroxide by the electrodialysis.