How does charging by induction work?

Let is try to understand this with the help of an example.

Let us have a metallic sphere and a negatively charged rod.
If we bring the rod near the sphere, what happens is that negative charges of the sphere due to repulsion start building up at the other end of the sphere leaving positive charges on the nearer end. However, not all electrons accumulated at the farther end : as negative charge builds up, the accumulated charges repel the other electrons and soon equilibrium is reached under the two opposite repulsive forces. A steady state is reached.

The rod thus induces positive charges in the near end and negative charges in the farther end. This is the process of induction and happens instantly, If the rod is removed, the charges again distribute themselves as before.

Now, if we ground the farther end of the sphere by means of a conducting wire, many of the electrons flow to the ground.
Then, we remove the charged rod and the sphere is then found to be positively charged.

Contrary to the process of charging by conduction, the negatively charged rod doesn't lose any of it's charge,