Yes, in a series circuit, the current is the same at all points in the circuit. In a series circuit, the components (such as resistors, lamps, or other devices) are connected end to end, forming a single path for the current to flow through. Since there is only one path for the current to travel, the current remains constant throughout the circuit.
This principle is derived from the conservation of charge, which states that the total amount of electric charge flowing into a junction must be equal to the total amount of electric charge flowing out of that junction. In a series circuit, there are no junctions apart from the beginning and end of the circuit, so the current remains unchanged as it flows through each component.
So, the current is the same at any point in the series circuit, and the value of the current is solely determined by the total voltage supplied by the power source and the total resistance in the circuit (as given by Ohm's law: I = V / R, where I is the current, V is the voltage, and R is the resistance).