I was asked a number of years again to start giving a daf yoni shiur in a local shul, without getting paid. Now I am ready to give it up? Do I have right to choose my replacement, or do the gabaim of the shul?
Since you were not being paid we can’t call it an official position or job. Additionally if it isn’t going to your son, there wouldn’t be any issue of Yerusha, therefore the shul or shiur has the right to choose the replacement.