He mentions it after battling him in his castle:
To Zekrom/Reshiram: "And Zekrom/Reshiram… thanks for everything. My journey with you has been truly wonderful! From now on, I want you to use your power to help this Trainer realize his/her dreams." "I know. I'll miss you, too... But your task is to help humans who seek ideals/truth. I learned so much from you. I'll do my best to tell everyone else what I learned on my own." "'I'll be OK! I can talk to Pokémon!" "I'll become the bridge between Pokémon and Humans! That's my ideal/truth!" "So… Rest well…" ", I'll entrust you with this Dark Stone/Light Stone!" "Take the Dark Stone/Light Stone to Dragonspiral Tower!" If talked to again "Go to Dragonspiral Tower. I will… I'll search for that Trainer I battled two years ago. And… I plan to say thank you."
And again, after the seasonal battles, after being defeated:
"I remember something Zekrom/Reshiram told me once…" "Zekrom and Reshiram are searching for new possibilities by walking alongside humans…" "Meanwhile, those that live in the wild try to better themselves without relying on anyone else." "There are many different Pokémon…" "And their different ways of living… That is the true freedom of Pokémon. That is what connects Pokémon to us." "I will set off on another journey." "There are still many Pokémon in the world I should talk to." "And there is also a Trainer I want to tell how I feel…"
So to sum up: