Do capacitors in series always have the same charge?

Consider two capacitors C1 and C2 connected in series to a battery. Is the charge going to be the same in them? The answer is yes and no. Most of the times you see the answer as yes. And the reason for that is that we assume that the initial charge in each one of them is zero. However, when the initial charge is zero or when the initial charge is same only then the final charge in them is the same. The reason is that actually it is the same charge that goes through the battery. Let's say the charge that goes through the battery is delta Q. Initially if capacitors are not charged this delta Q will appear in C1 and this delta Q will appear in C2. Now suppose that initially each one of them had charge Q. Again delta Q will go through the battery. So, final charge in C1 will be Q + delta Q and final charge in C2 will be also Q + delta Q. Now suppose that C1 has initial charge Q1 and C2 has initial charge Q2. Again the same charge will go through the battery. Let's say it is delta Q again. The final charge in C1 will be Q1 + delta Q and the final charge in C2 will be Q2 + delta Q.