RobH_en_tn/mat/10/41.md

because he is a prophet

Here "he" does not refer to the person who is welcoming. It refers to the person being welcomed.

a prophet's reward

This refers to the reward that God gives the prophet, not to the reward that a prophet gives to another person.

he is a righteous man

Here "he" does not refer to the person who is welcoming. It refers to the person being welcomed.

a righteous man's reward

This refers to the reward God gives to a righteous person, not a reward that a righteous person gives to another person.