Thanks for you're help but i don't know if i have talked whit her what are the sign the can tell me that i have talked to her
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She has her own little house in New Alexandria with a wooden sign next to the door, once you talk to her, you have to go to Deino's dinner first to grab something and then return to her. After that I think it's pretty straight forward, head to the frozen ruins location and meet up with her. You will then be told you need to catch a specific Pokémon that has 3 types. (You need to get very far in the game to find the Pokémon you need) Once you return to Emma at the frozen ruins with the pokemon, you will then be able to catch Emma (It's very easy to shiny hunt her, there is an NPC in the school that can tell you how to shiny-chain pokemon using vore moves, same room where you buy pred balls) After that the mini side quest ends and you will now have Emma to use in your party.