All persons holding administrative positions in the City government at the time this Charter takes effect shall continue in such positions and in the performance of their duties until dismissed or removed by the Mayor or other empowered authority. The powers conferred and the duties imposed upon any office, department or agency of the City by general law shall, if such office, department or agency be abolished by this Charter or under its authority, be thereafter exercised and discharged by the office, department or agency designated by Council unless otherwise provided in this Charter.