How does Telemachus know that the beggar is divinely favored in The Odyssey?
I assume you are talking about the part in Book 16 of the Odyssey where Odysseus appears to his son, Telemachus, while he (Odysseus) is disguised as a beggar. He has been disguised by Athena.
After talking to Telemachus for a while, Odysseus is told by Athena to reveal his true identity to his son. When Odysseus does that, Telemachus thinks Odysseus is a god.
Telemachus thinks this because he can't believe that a mere mortal could just go out the door and then come back looking younger and wearing different clothes.