This statement is false. Homologous structures will have different functions in various species although there are times when there may be some similarities. For example, the leg of a dog and the whale’s flipper are considered to be homologous with each other but this does not mean that their functions are the same.
The flippers will be used by the dolphins in order to move around while dogs would use their legs in order to walk and run. Another known example is the wing of the bird with the human arm. They are homologous but birds use their wings in order to fly while humans cannot fly. Arms are used in order to do different functions that human beings need.