Is it permissible for the muezzin to split the reward for the adhan with another person who helps him with it?

It is permissible to give a portion of your remuneration to whoever helps you with the adhan, whether he actually helps you or not, as long as the adhan is established in the mosque at all times. If the entity providing the remuneration does not accept anyone else's adhan, then it is not permissible for you to miss the adhan except for an overwhelming necessity, and your absence should be with their permission.