Henry wants to “install[]” Edward on the throne, which really means he wants Edward to start taking on a more active role in preparation for becoming king. If the people see Edward showing up to certain events in the king’s place, it will be easier for them to accept Edward as a king when Henry dies. Henry’s comment that the prince has always had a kind and compassionate heart emphasizes the fact that Edward and Tom’s resemblances are not just skin deep, but extends to their fundamental characteristics and values, too.